1-Intro-OT/Exercice-Somme-de-deux-gaussiennes.ipynb

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    "# Somme de deux variables gaussiennes"
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    "- Create the `Normal` distribution $X$ with parameters $\\mu=-5,\\sigma=3$\n",
    "- Create the `Normal` distribution $Y$ with parameters $\\mu=5,\\sigma=3$\n",
    "- Create the multivariate `Distribution` with marginals $X$ and $Y$ and independent copula\n",
    "- Create the `RandomVector` input random vector `inRV` defined with the distribution\n",
    "- Define the symbolic function `f` such that \n",
    "$$\n",
    "f(x,y)=x+y\n",
    "$$\n",
    "- Create the `RandomVector` output random vector `outRV` as composition of `f` and `inRV`\n",
    "- Create three sample with sizes `N=100,1000,10000` of the output random vector `outRV`.\n",
    "- For each sample, compute :\n",
    "\n",
    "  - The mean,\n",
    "  - The standard deviation,\n",
    "  - The quantiles of level $\\alpha$=`0.05,0.50,0.95`. \n",
    "\n",
    "- Now instead of the `Function` and random vectors, use the `+` operator to define the variable `Z=X+Y`.\n",
    "\n",
    "- From this distribution `Z`, compute :\n",
    "  - The mean,\n",
    "  - The standard deviation,\n",
    "  - The quantiles of level $\\alpha$=`0.05,0.50,0.95`. \n",
    "- Compare the two results: which one is more accurate?"
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