Add notes for Pd and Pfa

src/sdr/_detection/_theory.py

@@ -577,6 +577,12 @@ def p_d(
  Returns:
  The probability of detection $P_d$ in $(0, 1)$.
 
+ Notes:
+ The probability of detection $P_d$ is defined as the probability that the detector output $T(x)$ exceeds the
+ detection threshold $\gamma$ given that the signal is present.
+
+ $$P_d = P\left(T(x) > \gamma \mid \mathcal{H}_1\right)$$
+
  Examples:
  .. ipython:: python
 
@@ -730,6 +736,12 @@ def p_fa(
  Returns:
  The probability of false alarm $P_{fa}$ in $(0, 1)$.
 
+ Notes:
+ The probability of false alarm $P_{fa}$ is defined as the probability that the detector output $T(x)$ exceeds
+ the detection threshold $\gamma$ given that the signal is absent.
+
+ $$P_{fa} = P\left(T(x) > \gamma \mid \mathcal{H}_0\right)$$
+
  Examples:
  .. ipython:: python