Blog.md

ECS 132 Blog

Spring 2023

June 14, 1345:

Message from Lan: "HW3 grades have been sent out. Can we have a blog post letting everyone send an email if they have questions about their homework grades? (No
regrade requests will be accepted btw.)"

June 6, 1645:

You may find the curve function useful. E.g. try running

curve(x * exp(-x),0,5)

June 5, 2125:**

I've decided to push back the due dates for the Term Projects in both my classes to June 13. I shouldn't extend it any further, so as to not affect your final exams much, and of course I need to read and grade all those Project papers before the campus grading deadline.

June 5, 1945:

Just to clarify the stat tutorial:

Say we are estimating a population proportion q, based on the sample proportion Q. For instance, think of the election example, where the candidate wishes to know what proportion q of the population will vote for him. The pollster takes a sample, and finds that a proportion Q in the sample say they will vote for him.

We would like to find an approximate 95% confidence interval for q, based on Q. This is actually a special case of finding a CI for a mean μ. Set X to be 1 or 0, depending on whether a voter likes this candidate or not. Remember, the average of 1s and 0s is the proportion of 1s. So μ is actually q, Ā is actually Q.

The tutorial notes that S² = Q(1-Q), so the standard error of Q is s.e.(Q) = sqrt(Q(1-Q)/n). In other words, the general CI for μ shown in the tutorial

(Ā - 1.96 s.e.(Ā),Ā + 1.96 s.e.(Ā))

reduces to

(Q - 1.96 sqrt(Q(1-Q)/n), Q + 1.96 sqrt(Q(1-Q)/n))

Of course, estimation of proportions arises often in applications. Say we interested the proportion q of all light bulbs whose lifetime is greater than 150 hours. (We are NOT assuming an exponential or any other parametric distribution here.) We take a sample of n light bulbs, and find the proportion Q of those lasting more than 150 hours, then use the above formula.

June 5, 1100:

Unless there is an easy closed-form expression for an MLE, use the mle() function. And note that that function does the work for you: You do NOT compute derivatives yourself, and you do NOT solve the resulting equations yourself.

June 5, 0930

Every question on the Group Quiz will come from the statistics tutorial. The previous material will be used for support, of course, but if you've been doing well on the Quizzes and Term Project, you will be fine. You'll need: Properties of E(), Var(); parametic distribution families (binomial, geometric, Poisson, negative binomial, uniform, exponential, normal, gamma, beta).

June 3, 1540:

The grades for Quiz 2, Thursday, were not sent out. I'll send it all again when I get to the computer that has those grades (lack of a git push). I'll include Quiz 0 too.

June 3, 1510:

The Quiz records I just sent out do not include Quiz 0

If you have a question about your records, OF COURSE it would be helpful if you were to state which section you are in, Tuesday or Thursday.

June 2, 1645:

Some people have asked me about the answer to Question 1 of our Thursday Quiz 7. Acceptable answers were density() and plot(density()), while plot() is not acceptable.

As noted in our class discussion of polymorphism in R, functions such as plot() and print() are not "real" functions, in that they don't do any work; they are just go-betweens. And more important, the real work of smoothing is done by density().

The polymorphism issue is important in its own right. Please make sure to read this writeup.

BTW, one of the most important things you can do to prepare for our Group Quiz is to look carefully at the solutions to both of the Quiz 7s, Tuesday and Thursday.

June 2, 1020:

In my in-class demo of R's hist() and density() functions, I remarked on possible outliers, and maybe removing them. It appears now that some students think that dealing with outliers is part of the Project. It is NOT part of the Project.

Ordinarily, your analysis will NOT mention outliers. If you have an example in which you wish to do so, you will need to give a firm justification for doing so, based on the inherent nature of the data source.

June 1, 2245:

If you answered

pexp(150,1/100)

Quiz6/Tues, you should have gotten full credit. Let me know if you didn't.

June 1, 2150:

A bit of clarification re the blog post of May 31, 1035:

• The term closed-form solution means an explicit formula. The equation x² -3x + 2 = 0 has an explicit solution, while x - e^-x = 0 does not. We must solve the latter iteratively.
• You will be able to find cloed-form solutions for the MM estimators in the examples here, but in some cases you'll need to obtain the MLEs interatively; use R's mle() function for the latter (see the stat tutorial).

May 31, 1110:

As I have mentioned, members of teams who submit a very good Term Project will be given a substantial bonus in determining their course grade.

The same is true for the Group Quiz. On one level, it counts in the course grading formula like any other Quiz. But again, members of teams who do very well on the Group Quiz will be given a bonus when I determine their course grade.

Like any Quiz, the Group Quiz is technically cumulative in scope, since the course material builds up continually through the quarter, but focuses on more recent material. In other words, earlier material may be used in current contexts, just we saw with use of mailing tubes for expected value and variance yesterday in class.

The main material covered will be continuous distribution families and statistics, and properties of expected value and variance.

The Group Quiz will assess your ability to integrate material from various parts of the course, and thus is of very high importance.

how the code used to compute it iteratively. May 31, 1035:

Tomorrow in class, I will skip ahead and discuss MM and MLE methods, which you will use in the Term Project.

In your Term Project report, you must show the equations used to compute the MM and MLE values for your data. (Of course, this means doing this once for each distribution family.) And, if an equation has a closed-form solution, show it; otherwise, show the code used to compute it iteratively.

May 30, 2135:

REMINDER: We will have our Group Quiz on Thursday of next week, June 8, during lecture. This is a key element of our course, so make SURE you've read the rules in the blog post of May 23, 2240 (attendance is required, NO use of the Internet--this includes cell phones--etc.).

May 30, 1915:

Message from Lan:

Hi, Norm,
Could you please make a blog post to announce the booking links of the
interactive grading sessions? Thank you very much.
Lan, [1]https://calendar.app.google/AcV3szMA8ov2xNeM9
Dylan, [2]https://calendar.app.google/JvX3VjWSAQ5gdPyY8
Also, since I have to attend the graduate student yearly assessment on
Friday, my OH on Friday will be using the zoom link included in my
booking link.

May 30, 0935:

This is a reminder that in your Term Project report, you must be very careful to distinguish between population and sample quantities, e.g. between the mean value of X in the population and the average of X in the sample, (X₁,...,X_n)/n.

May 28, 2240:

The Central Limit Theorem says, roughly, that sums of random variables have approximately normal distributions. The basic form says that if X₁, X₂, ..., X_n are IID, then X₁+X₂+ ...+X_n has an approximately normal distribution with μ = EX and σ^2 = Var(X). The larger n is, the more accurate the approximation.

So for example if X₁, X₂, ..., X₁₀₀ is a sample from a population in which X has mean 52 and variance 2.4, then W will have an approximately normal distribution with mean 5200 and variance 240.

The formal theorem says that the cdf of (W - n μ) / (n^0.5 σ) converges to that of a N(0,1) random variable as n goes to ∞.

May 28, 2050:

For this coming week's Quizzes, make sure you understand the stat tutorial, through the lesson on confideence intervals, both in terms of interpretation and implementation. Concerning the latter, make sure you can access data in R, up through the lesson on data frames.

May 27, 1545:

A student asked me today that about the amount of writing in your Term Project report. I had previously said you'd have a lot of writing to do, but from the Term Project specs it looks like there isn't much. Here is the situation.

Actually the project I gave you is somewhat scaled back from what I originally planned. There was going to be a second problem, with a considerable amount of writing.

Nevertheless, your writing in the report must be done very carefully and thoughtfully. You will explain specifically and in detail what you're trying to do and how you did it, and then explain the results. There still will be a non-trivial amount of serious writing.

One thing that definitely has not changed is my statement in class that you have to make sure you don't say anything that is conceptually incorrect. For instance, failure to distinguish between a population quantity and its estimator is a serious, fundamental error.

Both in the Term Project and in our remaining Quizzes, keep at the forefront of your mind the interpretation of the concepts. For example, on Thursday, we discussed the following:

Say T is an unbiased estimate of some population value θ, meaning ET = θ. This means over all possible samples of size n from this population, T is sometimes less than θ, sometimes greater tan θ, but on average working out to exactly θ.

Now, couple that with a situation in which Var(T) is small. The small variance means that T doesn't vary from one sample to another, and since the values of T are centered at θ, that means in most samples T will be near θ. In turn, that means that the probability of T being near θ is high.

You won't find the above point in any book. The authors of the books do know this, of course, but they don't realize that the readers may not see what is going on.

And of course if the readers, for their part, are just memorizing the mechanics of statistical procedures, there is no hope that they'll understand. Our remaining Quizzes, and the writing standard for your Term Project, will focus on understanding.

I mentioned in class that statistics is hard, actually harder to understand than Markov chains. This may surprise you; how hard can it be, given that this material is in a high school class? But the interpretation is crucial, and in turn statistics is crucial to our lives. It affects how much you are charged for insurance, what kinds of medical treatment you get, how the government manages the economy, and so on.

The importance of this material greatly transcends the grade you get in this class.

May 26, 2140:

News items:

• Next week, the week of May 29, we will have our discussion section Quizzes as usual. Coverage will mainly be on the statistics tutorial, but may also include variants of Quiz questions from this past week.

• During the week of June 5, we will not have discussion section Quizzes, and in fact the discussion sections will not meet that week. However, we will have our major Group Quiz during the lecture time slot on June 8. Make sure you've read the blog post of May 23, 2240.

May 26, 1020:

I corrected the typos in Lesson BIAS in the stat tutorial, mentioned in class yesterday, and have added a bit of wording.

May 25, 1805:

I added the missing material on the data repo.

May 24, 0945:

We began the tutorial on statistics yesterday, and will be using it in our remaining lectures. In Quizzes, including the Group Quiz, you will need to have both this document and our textbook on your machine.

May 23, 2240:

Keep in mind that our Group Quiz will be held in the last lecture, June 8.

• You will have the entire 70 minutes.

• You work with your Group, and submit just ONE quiz.

• Note: Attendance is required.

• I suggest sitting on the floor, maybe bringing your own portable chairs, etc. to facilitate interaction.

• It will use OMSI, as usual. Write your e-mail address in the usual ajones.bsmith.clee format, as in our homework. Make SURE to get this right. The usual rules apply: No use of the Internet but the Quiz is open-book, open-notes.

• The Quiz problems will be similar to what we've had, but somewhat more
  elaborate. There probably will be 3 problems for the 70-minute Quiz.

• It will be noisy, maybe even fun. But it's a serious Quiz, and counts just like any other.

May 23, 2140:

I've finished grading the Thursday Quiz 5. Sorry for the delay.

In general, I was very pleased at how well you did on that Quiz (both days).

As we now near the end of the quarter, please keep in mind the "bonuses" that can boost your course grades:

• Your lowest 3 Quizzes (in letter grades) will be dropped.

• An excellent Term Project can bring a major boost to your course grade. (See the example in the course Procedural Information document.)

An example of noncompliance is being a No-Show at a scheduled interactive grading session. I'm told that there have been a number of such incidents, something that did NOT happen in the many earlier times I've taught this and other courses. Of course, one might have a valid excuse for missing a scheduled grading session, but apparently the students in these cases are not even offering excuses. They will not get credit for the assignment, and if a student is a multiple No-Show, he/she will fail the course.

May 22, 1930:

If you missed class last Thursday, note that I discussed the Central Limit Theorem and the"memoryless" property of the exponential distribution family. What I presented was material in Sections 7.10 and 8.2, though much briefer than what is in those sections.

May 22, 1920:

Lan will be away at a research conference this week. Dylan will sub for him in tomorrow's discussion section. Lan will hold his Wednesday office hour on Zoom, using the link he used before. His Friday hour will be canceled.

May 22, 1350:

I fixed an ambiguity in Problem 3. Each call currently in service terminates with probability p. Calls on hold do not terminate.

May 22, 1330:

A student asked a question re Problem 3. My answer was,

If we are currently in state r+3, i.e. r calls in service, 3 waiting, then the biggest drop would occur of all r calls terminate. The 3 waiting would then be in service, i.e. we are in state 3.

May 22, 1255:

For this week's quizzes, know the "d,p,q,r" functions backwards and forwards. Know not only their call forms but also how to use them to solve problems. Make up your own problems as practice!

May 21, 1720:

Thanks to an alert student, I just corrected a typo in Problem 3. Only one new call (or none) can arrive in any epoch.

May 21, 1410:

After we finish the current chapter, the rest of the course will cover my tutorial on statistics, something like the first 10-12 lessons. (They're short.) This material will appear on Quizzes, and will be vital to your Term Project.

Concerning the latter, recall from the Project specs that proper interpretation will be vital, especially in your written report. Issues of interpretation will be a major focus of the stat tutorial. It is not enough to merely understand the mechanics of the formulas etc.

May 21, 0935:

REMINDER!

As noted multiple times in class and in the class Procedural Information, all of your ECS 132 course records are indexed by your official UCD e-mail address. This is the address at which you have been receiving my blog announcements, for instance. If you submit Quizzes, Homwork and the Term Project under any other address, you risk having the work overlooked. This can adversely impact your grade, and possibly even cause you to fail the course.

Soon I will be e-mailing you a list of all Quiz grades I have for you. Check it carefully!

May 19, 2250:

The Term Project is ready!

As noted before in the course Procedural Information, very good Term Project submissions result in each student in the team being given a bonus in the computation of the course grade.

Start now! The earlier you start work on the Project, the more likely it is that you do good enough work to obtain this bonus.

May 17, 1525:

I've gotten several requests for makeup sessions for missed interactive grading sessions. I've approved them so far, but will stop doing so, except for seriously extenuating circumstances.

The TAs are very busy with the work they already have, and of course they have their own coursework to deal with. It is inconsiderate of students to ask them to hold extra sessions.

Missing an IG session is just as serious as missing a quiz.

May 16, 2110:

If your answer to Question 3 in today's Quiz was 2, you likely should get full credit. Please contact me.

May 16, 1635:

Either today or tomorrow, I will be posting the specs for your Term Project. Note the following:

• Due June 11. (Think of it as "Problem 4" of Hwk 3.)
• A professional-quality written report, prepared in LaTeX, will be required.
• Though you'll write some supporting code, this is not a coding project. It is analysis, with an emphasis on interpretation.

May 15, 1635:

For some reason, lately I've gotten a number of requests from students who wish to take a Quiz in the section in which they are not enrolled. E.g. students in Lan's section want to take the Quiz in Dylan's section.

I've been saying yes, but sorry, I will have to stop doing so. We don't want to risk exceeding room capacity, and we don't want to burden one TA more than the other in terms of proctoring etc.

May 15, 1535:

I've mentioned a few times--a couple of times in class and in the course Procedural Instructions document--that

• we will have a (required) Quiz in lecture, on the last day of lecture, June 8, and
• that Quiz may take the form of a Group Quiz.

I've decided to make it a Group Quiz rather than individual. In other words, during 10:30-11:50 a.m., June 8:

• You will sit together with your Group teammates.
• You will use OMSI as usual.
• You will collaborate on the Quiz with your teammates, and only submit
  one set of Quiz solutions.
• In collaborating with your teammates, you are allowed to talk.
• Same conditions as usual: Open book, open notes, no consulting anyone outside your group, no Web use.
• Topical coverage as usual: Focus is on the recent course material, but is cumulative in the sense that later parts of the course make use of earlier parts.

May 15, 1335:

Here is some important information regarding the recursion problem in Hwk 2.

Focus here on the principles, not the coding. In particular, take note of the "probability-ish" solution, as opposed to the "CS-ish" one.

The latter involves counting possible paths in a tree, leading to a combinatorial analysis. Good, but it is not generalizable. What if, say, some tags are more likely to be chosen, say because they are bigger in size? And equally important, the combinatorial approach does not relate much to probability. (Cf the hints given in the blog.)

Let T denote the number of tag draws needed. We are asked to find P(T = s).

The hint said to, as usual, "Break big events down into small events," asking "How can it happen?" Well, break things down according to F, the number on the first tag that we draw.

P(T = s) = Σ_i P(F = i, T = s) = Σ_i P(F = i) P(T = s | F = i)

P(F = i) here is 1/m (but this is generalizable). What about P(T = s |F = i)?

WELL, THAT IS THE KEY TO THE RECURSION! The reason is that

P(T = s | F = i) for our original value of m is the same as P(T = s-1) with m replaced by m-i. In other words,

tags(m,k,s) = Σ_i (1/m) tags(m-i,k,s-1)

This is exactly what we want with recursion of some function f--an equation in which on the left side we have the value of f with some arguments, and on the right side we have one or more instances of the alue of the function with some other arguments. That gives us our code:

tags <- function(m,k,s) 
{
   if (k <= 0) return(0)
   if (s == 1) {
      if (k > m) return(0)
      return((m-k+1)/m)
   }

   tmp <- 0
   for (i in 1:m) {
      tmp <- tmp + (1/m) * tags(m,k-i,s-1)
   }
   tmp
}

May 15, 0935:

Make sure you are ready to use the R function integral on Quizzes. Example:

> z <- integrate(function(x) x^2,1,4)
> str(z)
List of 5
 $ value       : num 21
 $ abs.error   : num 2.33e-13
 $ subdivisions: int 1
 $ message     : chr "OK"
 $ call        : language integrate(f = function(x) x^2, lower = 1, upper = 4)
 - attr(*, "class")= chr "integrate"
> z$value
[1] 21
> integrate(function(x) 1/(x^2),1,Inf)$value
[1] 1

Note carefully that integrate() does NOT directly return the value of the integral. An R list is returned, with the value as one of the components.

May 14, 2035:

Further tips:

• Make sure you are ready to use the R linear algebra functions.
• We will likely have at least one problem similar to one of last week's problems.

May 14, 1315:

Tips for this coming week's Quizzes:

• The earlier you get a good start on Hwk 3, the better you will do on your Quiz.
• Almost all questions will involve Markov chains.
• There will be at least one question involving the 3-Heads-in-a-Row game. Try to think of questions for it! Just thinking of questions will help you solidify your understanding of the material.

May 13, 2050:

Message from Dylan:

This homework, we've added more time slots, making it so that there are
more remaining slots after every team has chosen a time, removing the
likelihood of any makeup interactive grading. Use the two links to
access the time slots (they all take place on Wed May 17 and Fri May
19):
[1]https://calendar.app.google/Wn3ois9ChPa4Pcxg6
[2]https://calendar.app.google/1Uqn8ZDmMAveSJuK6

May 12, 2120:

The specs for Hwk 3 are now complete.

Problem 1 is fairly easy, in the sense that you are well familiar with the context, the parking space example. It does involve infinite series, though, so it will take careful concentration.

Problems 2 and 3 involve Markov chains. Though we will continue our coverage of Markov chains next week, you already have all the background you need for these problems.

I've said that the topic of Markov chains is probably the most difficult we've covered so far. Accordingly, you may at first find this assignment to be somewhat more challenging than the others, but as long as you start early you should be able to work the problems correctly.

Please heed the exhortation of April 18, 2045:

Each member of your Group should make a serious start on a Homework assignment 1 week before the due date AT THE LATEST, and should get together at that time to plan how to operate in the remaining time.

If you wait too long to begin, you likely will not finish.

May 12, 1645:

Problems 1 and 2 of Hwk 3 are now on our repo. There will be at least one more. Tentative due date May 19.

May 10, 1705:

You will recall that I said that one or more problems from last week's Quizzes would show up (slightly modified) in this week's Quizzes.

I've mentioned that the concept of independence is one of the really core concepts in probability, so it's not surprising that yesterday's Quiz included a question of the same form as Question 1 on last Tuesday's Quiz; it gave four pairs of random variables, and asked which are independent.

I was very pleased to see that most students yesterday did indeed get this one correct. But I was baffled to see that most of those who got it right incorrectly assumed independence in another question--one that involved random variables that the textbook even stated were not independent.

Please give this some thought, especially in terms of how you might avoid such a scenario in future Quizzes.

May 10, 1640:

Pro tip: In a Quiz, if you get a number larger than 1 for a probability, something is wrong. :-)

And that's one of the advantages of using OMSI. You can run your code, and SEE there is a problem in such a situation.

May 8, 2010:

Some tips regarding Problem 3.

• A recursive algorithm exploints a mathematical relation. Your first job must be to develop that relation. DON'T WRITE ANY CODE YET!

• So, you must develop a mathematical equation first. Keep your laptop closed! Stick to pencil and paper.

• The equation will be something lib f(n) = f(n-1) + f(n-2) for Fibonacci numbers. Note the form! The function is being evaluated on both sides of the equation, but with different arguments. Your job is to find such a relation for tags().

• To guide your intution, work out a small case by hand, again using pencil and paper. Ask our famous question, "How can it happen?" and then follow our famous path, "Break big events down into small events."

• You'll have ands and ors. The latter will bring you sums, and the former will then be converted with the mailing tube P(A and B) = P(A) P(B | A).

• The key will be to recognize that P(B | A) here will actually be tags(), evaluated at new arguments! That's how you'll get a Fibonacci-like relation. The coding will then be easy, though the base case might be a little delicate. Just implement your equation, just like the Fibonacci number case. Do NOT think of the tree of calls that occur; the language, in this case R, handles that for you, behind the scenes.

• Your first try will likely be incorrect, resulting in either wrong answers or a never-ending call chain. In debugging, start with a small case, and WALK THROUGH YOUR CODE USING A DEBUGGING TOOL!!!!

May 8, 0920:

As noted in class, you should devise little experiments to check your understanding of various functions and concepts.

For instance, suppose you are not sure what the p** functions do, e.g. pbinom. Try a little call on the R command line, say:

> pbinom(1,2,0.5)  # does this really give the probability of at most 1 head out of 2 tosses of a coin?
[1] 0.75  # yes

May 6, 0810:

In Question 2 of the Thursday Quiz, the 4 parts were not graded separately, but rather in terms of the overall view of how a student's answers reflect general understanding of the course concepts. If you had 3 of 4 parts correct, you should have gotten 10 or 15 points; if you got only 5, please let me know, and I'll correct the score, and also correct the letter grade if it changes under the new score.

BTW, note that in computing course grades, your letter grade is all that counts; your actual numerical score does not enter into the computation. Again, see the course Procedural Information site for this and other important information.

May 5, 2320:

The grades for the Thursday Quiz 3 have been mailed out, and the solutions posted on our repo.

Scores ranged from 5 (1 student) to 100 (4 students), out of 50 who took the Quiz.

If you feel you were undergraded on some problem, please feel free to contact me, and I will take another look.

Again, make sure you read the blog posts of May 5 0925 May 4 1050; and May 2 2135, with important information about Quizzes and course grade policies.

May 5, 0925:

Important news regarding Quizzes:

• I mentioned that sometimes in a course, I drop the lowest 3 Quizzes, rather than 2. I've decided to do so for our course.

• In Quiz 4, at least one question will be a variant of one in Quizzes 3 (could be either Tuesday or Thursday).

• In Quiz 4, at least one question will involve the parking space example.

May 3, 1955:

The following may help you visualize Problem 2 in our Homework.

Say you're the host. Prior to the time of the game, you've got to decide:

• (a) how many prizes to have (there was just one in the original example)

• (b) what value prizes do you want to have

• (c) which doors you want to place the prizes behind

Your decisions regarding (a) and (b) are then the vector v.

You will randomly choose doors for (c), and these door numbers are then the vector A. (Remember, in the original problem, A was just a scalar, but now it is a vector, of the same length as v.)

As host, you'll need to have at least two doors with no prize behind them. This is necessary, because in tempting the contestant to change her mind, you'll open a door other than the one she guessed but also other than the ones that do have prizes. This forces the length of v to be less than or equal to d-2.

May 3, 1050:

I plan that next week's Quizzes, both Tuesday and Thursday, will include problems in the setting of the committee example covered in yesterday's lecture. The questions will cover new concepts, e.g. probability mass functions, but in the context of that example.

For instance, a question could ask:

Write a function with call form pmm(k) that returns the probability mass function of the random variable M in the committee example.

The solution would be

pmm <- function(k) 
   # number of possible committees with k men and 4-k women),
   # divided by the number of all 4-person committees
   choose(6,k) * choose(3,4-k) / choose(9,4)

May 3, 1035:

There is a wealth of further examples for our course in our old Quizzes, including solutions. Though I previously gave you a link to all the files, I have now uploaded them to our GitHub repo for your convenience.

You can clone the repo on your local machine, and among other things do grep searches. For instance, yesterday we covered the concept of probability mass function in lecture, and you may wish to see how that notion might turn up as a Quiz question. So you could run

grep 'probability mass function' *Questions.txt

and then look at the questions that grep finds, if any.

May 3, 0815:

If you had an answer of 0.25 for Problem 4 on yesterday's Quiz, you will get full credit. Please e-mail me.

May 2, 2135:

The Tuesday Quiz 3 is now graded, and solutions placed as usual in our GitHub repo. Scores ranged from 0 to 90 (there were several at both ends of this range). A few comments:

• Problem 1 relied on just an intuitive understanding of independence, and it was placed at the first problem, generally intended as the easiest. It was not difficult, but it did have its subtleties. For example, the pair of random variables in choice (a) was NOT independent; the attachment action of v3 will affect that of v4, since the probabilities faced by v4 will depend on what v3 does. If you got at least 15 points here, consider that a good score.

• Problem 2 was a very straightforward application of our basic E(X) formula. The vast majority of you got this right.

• Problem 3 was a slight variation of an example in class. And by the way, that example in class came from a question that a student asked in class.

• Problem 4 just used mailing tubes, but required a lot of computation. I think that many students just ran out of time.

I should review how our course grades work:

• The basic formula is

  course grade = 0.60 x Quizzes grade + 0.20 x Homework grade + 0.20 x Term Project grade

• Your 2 lowest quiz grades (letter grades) are thrown out. In some courses, I actually end up deciding to drop the lowest 3.

• Term projects (done in your Homework Groups) of high quality are heavily rewarded, boosting your course grade 2 or even 3 notches about what the above formula gives. (A notch is a + or -, e.g. an A is 2 notches above B+.) Just yesterday I was showing some colleagues an example of a student in a previous course that had Quiz grades of D, A, C+, C+, A-, C, B- yet actually ended up with an A in the course.

May 2, 1800:

A couple of students asked me whether they could use helper functions in Problem 3. The answer is yes, providing your solution is recursive. However, my recommendation is to NOT do so; it isn't necessary, and you probably would just needlessly make things more complex.

Note: Though the function tags() is a probability, it still is a function. Thus the principle is no different from, say a recursive computation of Fibonacci numbers. You need to construct an equation (write an equation first, NOT code yet) that expresses tags() evaluated at m, k and s in terms of tags evaluated at one or more other sets of parameters.

May 2, 0955:

Please read the important message below from Lan right away. Also, NOTE CAREFULLY that during interactive grading, you will be asked questions both about your homework submission and about the course in general. The latter is just as important as the former.

"Dylan has created a time slot booking page on Google Calendar for interactive grading...We plan to have interactive grading happening at May. 3rd 1-4 pm, May. 5th 10 am - 3 pm, and May. 8th 1-4 pm."

May 1, 2045:

In interactive grading, each group will be asked different questions, but there may be some overlap. Do not divulge to other groups the questions asked of you.

May 1, 1550:

I have added clarification to Problem 2.

Also, in Quiz 1, Tuesday section, if you answered (2.2) to Problem 1 but did not get credit, let me know and I'll fix it.

April 30, 1530:

Earlier I stated that the statement of Problem 2 in the Homework would be changed. It is now changed, and ready for your work.

April 30, 1010:

In last Thursday's lecture, I mentioned the subject of course grades varying widely from one instructor to another. In that light, note that I gave some numerics regarding my own grading standards, in our FAQs. You may wish to review that statement.

April 30, 1005:

R's repeat function is very useful for building certain types of vectors, e.g.

> rep(8,3)
[1] 8 8 8

April 30, 0940:

In the coming week's Quizzes, make sure to be ready to compute the expected value and variance of quantities in our examples, e.g. E(L1) in the bus model.

April 29, 2330:

The function tag() is a probability:

tags(m,k,s) = P(it takes us s tag draws to accumulate a sum >= k)

Note that this is an unconditional probability, rather than a conditional one, though some conditional probabilities will turn out to play intermediate roles.

As you know, recursion involves finding a relation between a function evaluated at one set of arguments, and the same function evaluated at other arguments. Our general solution pattern of "break big events into small events" will be prominent in the solution.

Recursion coding is often challenging. I strongly recommend that you review how recursive function calls work (e.g. ECS 36C or its community college equivalent, whatever course you took) before starting on the problem.

April 28, 1335:

Very sorry, but I will have to change the wording of Problem. Please don't work on that one yet.

April 28, 1020:

I've pushed back the Hwk 2 due date to May 10.

April 27, 1605:

Some remarks on IDEs:

An IDE should make one more productive, not less.

In general, I am not a fan of IDEs. I've tried many, many of them, in languages C/C++, Python and R, and have always found that I am much more productive by just using the Vim text editor--WITH my homegrown Vim macros.

In R, for instance, if I want to write a 'for' loop, I just type 'frl', and Vim automatically expands it to

for (i in 1:n) {
}

To create a matrix, I type 'nmm', and Vim give me

matrix(nrow=,ncol=)

Small things, yes, but it saves me time, allowing me to focus better on the coding itself, and avoids future arthritis in my fingers. :-)

Of course, Vim automatically supplies me (in base form, i.e. not needing my own macros) with syntax highlighting, code completion etc., which the IDEs do. But the IDEs don't give me the ability to write macros.

Most of my macros are 1- or 2-liners, very easy to devise, but Vim actually allows you to write more elaborate macros in Python. Note, I didn't mean one's usage of Vim to edit Python; instead I'm talking about using Python to extend Vim, for usage in editing files in any language. Indeed,Vim plugins tend to be written in Python.

So the big advantage of Vim is that it allows me to customize my work environment, whether it be for my work in R, Python or LaTeX.

Obviously this is a matter of keen personal preference. Most professional deelopers do use an IDE, but many use Vim. The latter is not just something thrown into a beginning programming class as a "historical example."

April 27, 1005:

Please note that when a quiz or homework problem states something like "Use function X, Package Y etc.", then it is a requirement unless it explicitly says it is a suggestion.

April 26, 1845:

I've stressed the importance of submitting work using the correct e-mail address--the one to which I send you the "New blog post" announcements--because all of our course records are indexed by that address.

If you use an erroneous address, it's vital that you let me know. I will fix it and you will receive full credit.

If on the other hand, I do not know about the error when I make out the course grades, it will be difficult to fix with a grade change later on. It "probably" will be fixable, but we can't count on what the campus does.

April 26, 1430:

Homework 2 is now ready!

Please heed the blog post of April 18, 2045, in the statement reading in part "1 week before the due date AT THE LATEST."

April 26, 0850:

Simon Adds:

One of the most important cocepts in programming languages is that of a strongly typed language. In C/C++, for instance, one must a variable and its type before using it, and there are definite rules about mixing types.

Languages such as Python and R are much looser, but even they can require much care on the part of the programmer. E.g.:

> f <- function(a,g) g(a)
> f(3,sqrt)
[1] 1.732051
> f(3,sqrt(12))
Error in g(a) : could not find function "g"

What happened? The second argument g of the function f was itself a function. In the first example, we used g = sqrt. Since sqrt is indeed a function, it worked fine. But in the second example, we used g = 1.732..., which is NOT a function, and things blew up.

So the distinction between a function f and a call to f is not a matter of pickiness; it is a practical issue, affecting whether code runs properly or produces an error.

Unfortunately, all this is complicated by the general custom in the CS field of using parentheses to signify functions. E.g. if h is a function, people often refer to it as 'h()', using the parentheses to tell people that h is a function. But as you can see, though one might do this in informal conversation, one must be very careful in actual coding.

This and the previous post address the fact that on Tuesday's quiz, many students incorrectly gave the replicate function as an example of a function that has a function argument.

April 25, 2045:

Remember the other day when I mentioned the kids' game, Simon Says, to illustrate the supreme necessity in the CS world for precise thinking? Consider this code snippet:

> args(replicate)
function (n, expr, simplify = "array") 
> replicate(5,sqrt)
[[1]]
function (x)  .Primitive("sqrt")

[[2]]
function (x)  .Primitive("sqrt")

[[3]]
function (x)  .Primitive("sqrt")

[[4]]
function (x)  .Primitive("sqrt")

[[5]]
function (x)  .Primitive("sqrt")

> replicate(5,sqrt(3))
[1] 1.732051 1.732051 1.732051 1.732051 1.732051
> class(sqrt)
[1] "function"
> class(sqrt(3))
[1] "numeric"

The second argument of replicate(), expr, is an R expression, something to be computed. Well, sqrt(3) can be computed, but sqrt cannot. In other words, Simon Says, "There is a huge difference between a function and a call to that function"; different animals.

April 24, 1430:

Following up on the post of April 18, 2300: In a line like

f <- function(x) x^2

the expression 'function' is actually a function! I like to say, whimsically,

"The function of the R function named 'function" is to build functions."

So here, on the right-hand side of the assignment, we build a function, then assign it to f.

And yes, the '<-' and '^' are functions too. E.g.

> 3^2
[1] 9
> '^'(3,2)
[1] 9

April 21, 1615:

Postscript: a major problem was that that print() call was incorrectly specified, missing the nreps argument. My bad. Most students just went ahead and added it.

In terms of questions you can ask the TA during a Quiz, it would have been quite reasonable to ask the TA, "Is the nreps argument missing here?" By contrast, please don't ask a question like "My code won't run. What's wrong?"

April 21, 1545:

Well, miscommunications can occur... :-)

In my blog post of April 20, 0950, I reminded everyone that in Quiz questions with R code answer, you MUST make sure your code runs and prints. It's no coincidence that in yesterday's quiz, there was an explicit print() call in the code.

Unfortunately, Dylan didn't notice that, and told students that they could comment-out the print() call. So, several students lost points even though their code was mostly correct.

Even more unfortunately, those students chose to believe Dylan instead of me! Dylan is a super-nice guy, but I'm offended. :-) Just kidding.

But there was more. The reason those students asked Dylan in the first place was that actually their print() call was wrong. IOW, those students were asking Dylan to debug their code for them--in a Quiz! Please don't do that.

Anyway, if you were one of those students, you are welcome to ask me to take another look at your solution, for possible increase in points.

April 21, 1500:

Sorry, I don't think my Homework submissions directions were clear. Put all your files, named Problem1.R, Problem2.R and so on, into a .tar file. Here's the part I didn't make clear, the file name. It consists of your official UCD e-mail addresses, separated by periods. So e.g. if a Group's members have UCD addresses 'ajones@ucdavsi.edu' and 'blee@ucdavis.edu', then your .tar name would be 'ajones.blee.tar'.

I've made corresponding clarifications in the Hwk 1 specs.

April 21, 1410:

Quiz solutions are now in our course GitHub repo.

April 20, 2015:

As I've explained in class, all your course records, which are handled by scripts, are indexed by your official UCD e-mail address. If you give some other e-mail address for some item (Quiz, Homework, Term Project), you risk not getting credit for it. The human grader MIGHT notice a problem, and correct it, but this is not guaranteed.

Please make sure you use the UCD address at which you have been receiving mail from me.

April 20, 0950:

I'm grading Quiz 1, Tuesday section, right now, and have a few comments:

• When a Quiz question says, "R code answer," it means it! Your submission will be executed by the grading script, and if your submission is English, the script will choke. If your submission has no output, the script will think your code was wrong. The human grader will take a look, but without output you already have trouble.

• Read the question carefully--extra carefully if you are not a native speaker of English. Words like "the," difference between singular and plural forms, etc. can make a big difference in meaning, and can serve as hints on how to solve the problem.

• Similarly, make sure your answer is addressing the question that was asked. If say you are asked about the square of a matrix, your answer should discuss the square. It may be important to also discuss the role of the original matrix, but only as preparation for discussing the square.

• If you are asked for the probability of something, rather than the approximate value, don't use simulation. The official course rules state,

Note for ECS 132: In numeric problems, exact answers are required, not simulation, unless the latter is specified.

I'll post some more comments later, after doing more grading.

BTW, remember that your two lowest Quizzes (in letter grades) are thrown out in computing your final course grade.

April 19, 2255:

Notes on debugging, both in general and in R:

• Don't use print statements to debug! Use a debugging tool.

• Any good IDE will have a built-in debugging tool, e.g. VS Code (Python, R, whatever) or RStudio (R). The developers of those IDEs put them there for a REASON!

• Or use the underlying debugging tool directly, e.g. gdb (C/C++), pdb (Python) or debug() (R).

• Use my Principle of Confirmation: Step through your code in the debugging tool. Check variables etc. as you go along, confirming that "what you think is true, IS true." Eventually, one will not confirm, and you will then have at least found the location of the bug.

April 19, 1645:

As I have said, all the Quizzes are open-book, open notes. You can bring in anything on paper you wish, say your Homework solutions, or incorporate them into the PDF file for your textbook.

April 19, 1415:

The other day, I mentioned I would be postponing the Hwk 1 due date, and I did change the actual homework specs file accordingly. But just in case someone didn't check thst file, I'll say it here too: The new date date is Friday, 11:59 pm as usual.

April 19, 0845:

In the Procedural Information document (linked to by the Syllabus in our class repo), it says, "class attendance is vital to doing well in the course." If you miss many lectures, it is likely that you will get a poor grade in the course. I do recognize, though, that sometimes it will be necessary for you to miss class. If so, you are welcome to e-mail me to ask what pages of the book I covered in that lecture.

One thing I mentioned in class yesterday is that I do not believe human intelligence has a genetic component, and thus everyone can do well in this class. If you do the reading nonpassively, spend thoughtful time on the homework, and yes, go to class, you will get an excellent grade in the course.

April 18, 2300:

A note on interpreted language and code speed:

Consider the code snippet

for (i in 1:n) {
   tot <- tot + x[i]
}

as compared to

tot <- sum(x)

making use of R's built-in function sum().

In that first snippet, there are function calls galore. As I mentioned in class today, '+' is actually a function!

2+3

is actualy

'+'(2,3)

But not only that, but also '[', '<-' and ':' are functions! R is definitely what is called a functional language.

Now, as you learned in ECS 50, function calls have substantial overhead. The arguments must be placed on the stack, followed by the return address. If the body of the function is short, then the overhead becomes a substantial fraction of the run time of the call.

Moreover, depending on implementation, in each iteration of the above loop, the R interpreter may be doing a lookup to determine where in memory x and tot are. That would be really costly. By contrast, if R were a compiled language, that lookup would be done only once, at compile time.

Similarly, the sum() function is straight C, so we (probably) have no further function calls involved.

Remember, when you do something in Python, say

$ python x.py

you are not executing x.py; you are running the Python interpreter, a C program that happens to be named 'python'. It does the various lookups needed for the lines in x.py. So again, slow, and again, a need to vectorize.

Some speed improvement is made by the use of Python byte code. When you "run" x.py the first time, it may produce a file x.pyc, containing the byte code. This is "machine code" for a mythical "Python machine." In subsequent runs, the Python interpreter will execute on the byte code, at least free of lookups, though still slow because it is running the Python machine. In recent years, the R interpreter has been doing something similar.

April 18, 2250:

To illustrate Bayes' Rule, look at Eqn. (2.38) and those following it.

Let's first rewrite (2.67) as

P(U | V) = P(U) P(V | U) / [P(U) P(V | U) + P(not U) P(V | not U)]

so that the B in (2.67) doesn't get confused with the B for bonus roll in (2.38).

On the left-hand side of (2.38), we have

P(U | V)

where U is B > 0 and V is R+B = 4.

Now look at the numerator of (2.40). It's

P(V and U)

which by our mailing tube is

P(V) P(U | V)

This already is beginning to look like (2.67). And in fact, the denominator of (2.40) is exactly the denominator of (2.67), again after applying the same mailing tube.

So, Bayes' Rule is just a formalization of what we did in (2.38)-(2.40) and in (2.64)-(2.66). In other words, it's just a short cut designed to save steps.

April 18, 2045:

As I emphasized in my message of April 14, 1820, Group collaboration is essential in this course. Today I had to contact one student to remind him/her of this.

Each member of your Group should make a serious start on a Homework assignment 1 week before the due date AT THE LATEST, and should get together at that time to plan how to operate in the remaining time.

As I have said, there may be some variability regarding math or coding skill among Group members, but everyone must do their best to participate. Remember, even if you think about a problem for a long time but don't come up with a solution, you will have greatly deepened your insight.

April 18, 1605:

Things apparently went smoothly for most but not all students in today's Quiz. Here are some announcements.

• Making Quiz 0 take-home was supposed to prevent OMSI problems in subsequent Quizzes. Maybe there were VPN issues for some students.

• There was also the issue of using a PDF viewer from within OMSI. As you know, disallowing the use of any apps besides OMSI is an anti-cheating measure in OMSI, e.g. to prevent a student from e-mailing someone during a Quiz etc. But I did not realize that Windows does not come with its own PDF viewer, and that Windows refers its users to the Web browser, which could be used for cheating. I actually was rude to one student after class in saying that students are not allowed to use a browser during a Quiz. I apologize to him for that, and told Lan that for today's Quiz only, students could use a browser. But everyone who is on Windows, please install Acrobat or whatever before your next Quiz, whether it be this Thursday or next Tuesday.

• If you are in the Tuesday section and had OMSI problems today, you can take the Thursday Quiz this week if you wish. Let me know before I grade today's Quiz, probably tomorrow evening.

• Make sure to do a full test of OMSI, where you play the roles of both the instructor (you run the server) and the student (you run the client). Run the server on CSIF and the client in a campus classroom, for the most realistic test. Be sure to test the PDF viewing aspect as well.

April 17, 2150:

Picture yourself teaching someone to program. You tell them about arrays, loops and so on. They then ask you, "When do I use arrays?" Of course you know there is no good answer, because programming is a creative process; there are no rules telling when to use arrays, etc. All you could tell this person is

Arrays, loops, if-then-else, and so on make up your programming toolkit. You then must think how to creatively combine these tools into code that accomplishes your goal. And it is indeed creative, as there are many possible code implementations that will accomplish your goal; different peple will come up with different code to achieve the same goal.

And that's true even more so for solving probability problems, conducting statistical analyses, and developing machine learning prediction models. It's a creative process. Your "toolkit" starts with the mailing tubes, and then on the distribution models, ML algorithms and so on. There is no "formula" for any of this. You try something, and if you find out it isn't useful, you try something else.

April 17, 2110:

Below are notes I made for a student during my office hour today.

The experiment here is to flip a set of 20 coins, each of which has probability 0.1 of heads. Let H denote the number of heads we get.

E(H)--by definition--is the long-run average in the H column of the notebook. We will later learn how to derive the fact that E(H) = 2 here, but for now, just take it as true (and intuitively plausible).

The second column is labeled "squared distance of H to its mean." Its mean is 2, so these entries are (2-2)^2, (11-2)^2 etc. Var(H)--by definition--is the long-run average of these squared distances.

As noted, a simulation merely puts into code what we have in the notebook. So for Hwk 1, Problem 2's question about E(W), we have a W column, and our code is finding the long-run average of this column. In code terms, we are simulating nDays days of bus operation, corresponding to nDays lines in the notebook. Our code will have nDays iterations, in each which we generate W and add it to our running total. Our (approximate value of E(W) is then that total, divided by nDays.

Now, what about Var(W)? In the notes in the picture, we would have squared distances as (W - E(W))^2, one on each line. Var(W) is then (approximately) the long-run average of those squared values. So our code would then have a second loop to compute this long-run average. The reason we would need as a separate loop is that the squares in the second column of the notebook depend on first finding the average of the first column.

However, there is a trick, which is a mailing tube that we will cover soon: For any random variable X, Var(X) = E(X^2) - (E(X))^2. So, in our first loop, we can find running totals of both W and W^2, obviating the need for a second loop. You are not required to use this trick, but you may do so if you wish.

MAKE ABSOLUTELY SURE YOU UNDERSTAND ALL THIS, THE "WHY" OF EVERY STEP RATHER THAN MERELY THE "HOW." This is vital to your doing well in the course. If you master this--i.e. get to the point at which you can cogently explain it to your classmates-- you will be will on your way to getting an excellent grade in the course.

Note: For the exact analysis in this problem, I had intended that you compute only 2 quantities, not 10. I've changed the problem to have you compute only the second and third quantities in the list.

April 17, 1830:

For any Quiz, the lecture and reading coverage is all material through the most recent lecture, but not the same day's lecture. For our class, the coverage for Tuesday Quizzes is the material through the preceding Thursday's lecture, while for Thursday Quizzes, it is the material through Tuesday of the same week.

April 17, 1635:

In my post of April 15, 1500, I introduced the new chat feature that Lan has added to OMSI. It makes asking questions during a Quiz very convenient for both you and the TA. I think you'll really like it.

However, Lan told me just now that you do need to use Python 3 for this app, not the old Python. So if you wish to use this app (it's optional), you'll need to install Python 3 on your machine, and of course make sure it's in your path etc.

Python paths, environments etc. can get pretty complicated. (To me, a drawback of an otherwise wonderful language.) For that reason, I always recommend installing miniconda, which will give you the Python package rather than just Python. Of course, you must still set your system's search path accordingly.

If you install the chat, make sure to test it on your machine, just like you tested OMSI.

April 17, 1545:

This is just a brief note to say I will be pushing back the due date for Hwk 1. I also will be posting some hints and so on, arising from questions students asked in my office hours today.

April 17, 1345:

Quiz questions will typically refer to page numbers, equation numbers, section numbers, example names and so on in the book. It is thus imperative that you have a copy of the book, either in printed or PDF form.

April 15, 1500:

Remember, on Quizzes your OMSI window (including chat box; see below) must fill your laptop screen at all times. If you think you will need a copy of this blog, or your Homework submission etc., you may bring paper hard copies to the Quiz (and for that matter, paper copies of anything else).

Lan has added a new feature to OMSI, in the files chatXXX. You can use this to ask the TA questions during Quizzes. To use it, update your OMSI directory (e.g. 'git pull origin'), and note the chatXXX files. You run the chat client like you do the OMSI client:

python3 chat_client.py servermachinename serverportnumber youremailaddress

This hopefully will work better than your raising your hand and the TA trying to walk through the seats to interact with you.

Needless to say, there are still questions the TA will not answer, e.g. "What page in this book is this?", "I don't know what this term from the course means," etc.

The PDF viewer and chat are considered part of OMSI, so having them on your screen does not violate the rule. But be sure to start both the main OMSI client and the chat client at the start of the Quiz.

April 15, 1035:

In Quiz problems designated as "R code answer," you are NOT required to write code that is short, efficient or elegant. Just make it work. And remember, OMSI allows you to test your code, a vitally important feature.

April 15, 0955:

A couple of trivia items:

• For some reason the Registrar's student roster site is down this morning. I noticed in the error messages I got from running Lynx that the site uses Adobe Cold Fusion, an early Web development tool that has gone through various new versions.

  The original inventor of Cold Fusion was JJ Allaire. JJ wrote it as an undergrad and sold it to Microsoft for millions. He then became a "serial entrepreneur," founding a series of successful startups.

  A few years ago, JJ decided that the R language needed an IDE, so he developed RStudio, and founded the firm of that name. He's an amazing guy (and very nice personally). He still loves coding, and spends a lot of his day in that activity, even though he is the CEO.

• I mentioned Bob Metcalfe in class. He invented the Ethernet, which added "Listen before talk" to the ALOHA network, and it became his PhD thesis (with complex probability analysis on every page). He then founded 3-Com, and the Ethernet became the industry standard.

  Well, now he has won this year's Turing Award, "the Nobel Prize of Computer Science."

April 14, 1820:

I must again emphasize the UTMOST importance of close cooperation with your teammates. If one of your teammates contacts you, you should reply right away, acknowledging receipt of the message. Give the sender an estimate as to when you can address his/her points. As I said in class, in someone turns out to be unreliable as a teammate, I will have to put that person into a 1-student team, i.e. by him/herself.

April 14, 1740:

Problem 2 uses the concepts of expected value and variance, which we have not yet covered in our course. Here is what you need:

• The expected value of a random variable X, denoted by E(X) (or EX if we just have a single symbol) is the long-run average value of X in the notebook.
• A function of X is a new random variable, and we can define its expected value similarly. E.g. E(X^0.5) is the long-run average value of X^0.5.
• The variance of X, Var(X), is the long-run average value of this function of X: (X - EX)².

Of course there are issues of interpretation etc., but this is enough for you to do the Homework problem.

April 14, 1530:

As you know, you can view the "man page" (online help) of an R function by using a question mark, e.g.

?ls

to obtain information about the ls() function. But you can also do this via a call to the help() function, e.g.

help(ls)

This could come in handy in an OMSI session. Just temporarily put your call to help() in the Answers box in your OMSI screen, then click Submit and Run.

April 14, 1440:

A student contacted me, unsure of Problem 2 in the Homework. I'll share my response with everyone here.

The entity p is a vector of probabilities, describing the behavior of the Li's. E.g. if p = (0.25,0,35,0.40), then for any i,

P(Li = 1) = 0.25,
P(Li = 2) = 0.40,
P(Li = 3) = 0.35

The quantity v is the travel a bus needs to reach the stop of our passenger of interest, starting from the main station. So, for instance if Bus 3 leaves the main station at time 12, it will arrive at our special passenger's stop at time 12+v.

Bus 1 leaves the main station at time L1;
Bus 2 leaves the main station at time L1+L2;
Bus 3 leaves the main station at time L1+L2+L3;
and so on.

W is the wait time for our special passenger. Varies from day to day.

The number k is a parameter in our analysis of this bus system. We are interested in P(W = k) for various values of k. You will find P(W = 1) "by hand," i.e. mathematically, but will write simulation code that will find the value of P(W = k) for any k.

April 13, 2240:

Thanks, everyone who replied to my Extra Credit challenge. Several people were correct. I will answer everyone individually tomorrow.

The basic problem was that ChatGPT computed P(A and B) instead of P(A | B), where A is the first die having < 3 dots and B is the dice total being > 8. This of course is a very common student error, and ChatGPT made the same error.

April 13, 2025:

I gave this request (Section 2.14.5) to ChatGPT:

Suppose three fair dice are rolled. Fnd the approximate probability that the first die shows fewer than 3 dots, given that the total number of dots for the 3 dice is more than 8, using simulation in R.

Here is what it gave me:

n_sims <- 100000  # Number of simulations
count <- 0  # Counter for events of interest

# Run the simulations
for (i in 1:n_sims) {
  # Roll three fair dice
  dice <- sample(1:6, size = 3, replace = TRUE)
  
  # Check if first die shows fewer than 3 dots and total dots > 8
  if (dice[1] < 3 & sum(dice) > 8) {
    count <- count + 1
  }
}

# Calculate the approximate probability
prob <- count / n_sims
prob

This evaluates to about 0.16, rather than the correct 0.23.

Extra Credit to the first person who can tell me where ChatGPT went wrong.

April 13, 2010:

An alert student noticed an "off by 1" error in Problem 2 of the Homework. I've made slight changes to the specifications of the bus system accordingly.

I've also added more detail on the submission procedure.

April 11, 1530:

I see that my wording in Problem 4 of Quiz 0 was confusing. The freeway trip itself is 60 miles, and this figure does not include the 1.5 miles on surface streets.

If you thought the 60 mile figure included the 1.5-mile trip, I am hereby instructing the TA to give you full credit if your solution is correct for this interpretation.

April 11, 0915:

It's important to distinguish between definitions and properties that follow from the definitions.

For example, the definition of P(A|B) is based on the "notebook," the long-run proportion of lines in which A occurs, among the lines in which B occurs. It turns out that that implies that P(A|B) = P(A and B) / P(B) (where again, the definitions of P(A and B) and P(B) are based on the notebook.

In many cases, you will have P(A|B) simply by intuition. For instance, say an urn contains 10 blue marbles and 4 yellow ones. We choose two marbles at random without replacement. Find (2nd marble is blue | 1st marble is yellow). Well, if the first marble is yellow, then we still have 10 marbles in the urn, but the total number is now 13. Since all marbles are equally likely to be chosen, the probability is 10/13.

Similarly, though the definition of independent events is P(A and B) = P(A) P(B), we often know two events are independent simply from intuition. In the marbles example, if the experiment is to choose two marbles with replacement, then the colors of the first and second marbles are independent.

April 10, 1515:

Due date for Quiz 0 has been postponed until April 14.

April 9, 2305:

Hwk 1 is now official. Please start early.

April 8, 2250:

Just uploaded a (very) partial version of the simulation code you will write in Problem 2.

Hwk 1 is still not official, but I will make it so as soon as I get feedback from the TAs. I don't anticipate any major changes at this point.

April 8, 2150:

Concerning Problem 1 of the homework (not official yet, but close), the point of the problem is to give you practice in interpreting P(A), P(A|B) etc. So, you find the probabilities directly. E.g.

> sum(ucb[1,2,]) / sum(ucb)  # P(admit and female)
[1] 0.1230667

Ask me or the TA if you have any questions on this.

April 8, 1410:

If you added the course once the quarter started, please note our class GitHub repo. Read the syllabus, and the linked information, especially the class procedures. Also, please note that it is required that you read the class blog every day.

April 8, 1100:

I've now added Problem 1 to Hwk 1. Again, still just a draft.

April 7, 1650:

I've put a draft of Hwk 1 on our repo here, in the Hwk directory. Just a draft, as the TAs and I need to check and refine it, but it will give you an idea of what homework will be like in the course. Approximate due date Apirl 18.

April 7, 0955:

We will not have a quiz next week. Instead, Dylan and Lan will give a mini-lecture. Of course any such presentation could be the subject of quiz questions.

April 7, 0945:

I've pushed the full version of our textbook to our class repo here. It is NOT required that you read it, but it is there in case you wish to read more about some topic. Also, our official version contains '?' symbols, which are references to material that is in the full book but not in our version.

April 6, 2150:

Office hours:

NM: M 2-4, 3053 Kemper
DC: MW 1-2, 47 Kemper
LJ: W 2-3PM, F 2-4PM, 55 Kemper (starting week 2)

April 6, 2020:

My op-ed on ChatGPT and statistics is now out. You may find it interesting.

April 6, 1905:

Can you answer this question: "How does a computer boot up?" Most CS students can't. And when I mention that to non-CS people, they are shocked that such a basic thing would be foreign to budding computer experts.

It's not your fault. This topic should, IMO, be taught in ECS 50 and/or 150, and usually is not, I believe. But yes, it is indeed a basic thing, something very important to know, as are "systems" issues in general. In the last day or so, for example, I've encountered several students whose trouble with OMSI seems to be related to lack of knowledge of environment variables such as PATH, knowledge that is taken for granted in real-world software development. It is not enough to just know how to code. Nor is it enough to ace the PATH questions on the ECS 36B final exam but then erase the material from your brain after the exam.

April 5, 1805:

Please see my ECS 189G blog post of 17:35, re seeking help, the Unix script command, etc.

April 4, 2010:

I mentioned in class today that anyone who considers him/herself to be well versed with computers should know something about client/server programming. If you haven't done this kind of coding before, I urge you to read my tutorial. You will NOT need this for our class, just something to back up your future claims of expertise. :-) And by the way, it will help you understand OMSI better.

April 4, 1830

Someone brought up the perennial R-vs.-PYthon-for-data-science issue in both of my classes today. In the afternoon class, I made a comment about random forests, which I will elaborate on below, but first I should make one point clear: Our course is not an R-in-probability-and-statistics class; it's a probability-and-statistics class, period. The emphasis is on the concepts and methods, not on the language. Keep in mind always: this is a MATH class.

At any rate, I mentioned in the afternoon class that IMO there are better libraries for random forests in R than in Python. In case anyone is curious, I would cite e.g. the grf package by the Stanford Econ and Stat people. The linear interpolation capability is especially important.

But again, though the grf package was developed in R (I think there is now a Python version, though not in sklearn), this was not because R is a "better" language but because Stat people tend to use R.

April 4, 1225

All my old ECS 132 quizzes are available here.

April 3, 2106

We will soon be forming our Homework Groups. Group size is 3 or 4. If you have 1 to 3 people you would like to be in a Group with, please so inform Lan Jiang (lanjiang@ucdavis.edu) by Friday, April 7, 11:59 pm (even if you are in Dylan's section). Otherwise, Lan will assign you to a group.

Details of how the Groups work are in the general course info doc. Note carefully that this document is vital to your success in the course, regarding homework, exams, grading and so on; please read it right away.

April 3, 2052

My earlier e-mail messages said our blog was on the machine Heather. Of course, that is incorect. The blog is the GitHub file you are now reading.

April 3, 2048:

Our course syllabus is now ready!

April 3, 2015:

It may be a couple of days before we have days/times/locations for office hours. For now, if you have questions about Quiz 0, please e-mail NM on quiz content matters, or your assigned TA (see Syllabus, available later this evening) on OMSI issues.

April 3, 1405:

All class announcements from this point onward will be made here in this blog, rather than by mass e-mail. When making a blog post, I will also try to send a message notifying you of a new post, but may not always do so. You are required to read the blog at least once per day.