diff --git a/M2/TP1-distributions-etu.ipynb b/M2/TP1-distributions-etu.ipynb
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@@ -0,0 +1,1019 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Introduction to `julia` for statistic\n",
+    "\n",
+    "To contact me, here is my email : [joseph.gergaud@toulouse-inp.fr](joseph.gergaud@toulouse-inp.fr)\n",
+    "\n",
+    "The files ares here : \n",
+    "\n",
+    "[https://gitlab.irit.fr/toc/etu-n7/julia](https://gitlab.irit.fr/toc/etu-n7/julia)\n",
+    "\n",
+    "directory M2\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## empirical cumulative distribution function, eCDF\n",
+    "### Exercise 1\n",
+    "1. Build the empirical cumulative distribution function\n",
+    "\n",
+    "Let $t$ a vector of reals and $x$ a real, then \n",
+    "$F(t,x) =$ the number of datas in $t < $ to $x$."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 33,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "3-element BitVector:\n",
+       " 1\n",
+       " 0\n",
+       " 0"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# use broadcasting\n",
+    "a = [1,2,3.5]\n",
+    "a .< 2"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 34,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "empirique([1.,2,3],1.5) = 0\n",
+      "\u001b[91m\u001b[1mTest Failed\u001b[22m\u001b[39m at \u001b[39m\u001b[1m/Users/gergaud/git-ENS/Julia-TSE/etudiants/M2/jl_notebook_cell_df34fa98e69747e1a8f8a730347b8e2f_W4sZmlsZQ==.jl:19\u001b[22m\n",
+      "  Expression: empirique([1.0, 2, 3], 1.5) == 1\n",
+      "   Evaluated: 0 == 1\n",
+      "\n"
+     ]
+    },
+    {
+     "ename": "Test.FallbackTestSetException",
+     "evalue": "Test.FallbackTestSetException(\"There was an error during testing\")",
+     "output_type": "error",
+     "traceback": [
+      "Test.FallbackTestSetException(\"There was an error during testing\")\n",
+      "\n",
+      "Stacktrace:\n",
+      " [1] record(ts::Test.FallbackTestSet, t::Union{Test.Error, Test.Fail})\n",
+      "   @ Test /Applications/Julia-1.10.app/Contents/Resources/julia/share/julia/stdlib/v1.10/Test/src/Test.jl:1000\n",
+      " [2] do_test(result::Test.ExecutionResult, orig_expr::Any)\n",
+      "   @ Test /Applications/Julia-1.10.app/Contents/Resources/julia/share/julia/stdlib/v1.10/Test/src/Test.jl:705\n",
+      " [3] macro expansion\n",
+      "   @ /Applications/Julia-1.10.app/Contents/Resources/julia/share/julia/stdlib/v1.10/Test/src/Test.jl:672 [inlined]\n",
+      " [4] top-level scope\n",
+      "   @ ~/git-ENS/Julia-TSE/etudiants/M2/jl_notebook_cell_df34fa98e69747e1a8f8a730347b8e2f_W4sZmlsZQ==.jl:19"
+     ]
+    }
+   ],
+   "source": [
+    "using Test   # for tests\n",
+    "\n",
+    "\"\"\"\n",
+    "   Compute de number of element in the vactor t less than a value x\n",
+    "   input\n",
+    "   t : Vector of Real\n",
+    "   x : Real\n",
+    "   Output\n",
+    "   Integer\n",
+    "\"\"\"\n",
+    "function empirique(t::Vector{<:Real}, x::Real)::Int\n",
+    "    # to complete and modify\n",
+    "    return 0\n",
+    "end\n",
+    "\n",
+    "\n",
+    "println(\"empirique([1.,2,3],1.5) = \", empirique([1.,2,3],1.5))\n",
+    "\n",
+    "@test empirique([1.,2,3],1.5) == 1"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 35,
+   "metadata": {},
+   "outputs": [
+    {
+     "ename": "MethodError",
+     "evalue": "MethodError: no method matching empirique(::Vector{ComplexF64}, ::Float64)\n\nClosest candidates are:\n  empirique(!Matched::Vector{<:Real}, ::Real)\n   @ Main ~/git-ENS/Julia-TSE/etudiants/M2/jl_notebook_cell_df34fa98e69747e1a8f8a730347b8e2f_W4sZmlsZQ==.jl:11\n",
+     "output_type": "error",
+     "traceback": [
+      "MethodError: no method matching empirique(::Vector{ComplexF64}, ::Float64)\n",
+      "\n",
+      "Closest candidates are:\n",
+      "  empirique(!Matched::Vector{<:Real}, ::Real)\n",
+      "   @ Main ~/git-ENS/Julia-TSE/etudiants/M2/jl_notebook_cell_df34fa98e69747e1a8f8a730347b8e2f_W4sZmlsZQ==.jl:11\n",
+      "\n",
+      "\n",
+      "Stacktrace:\n",
+      " [1] top-level scope\n",
+      "   @ ~/git-ENS/Julia-TSE/etudiants/M2/jl_notebook_cell_df34fa98e69747e1a8f8a730347b8e2f_W5sZmlsZQ==.jl:2"
+     ]
+    }
+   ],
+   "source": [
+    "# If the type of the vector elements is not a real then there is an error\n",
+    "println(\"empirique([1.+2im,2,3],1.5) = \", empirique([1.,2+2im,3],1.5))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "2. Generate a sample of N=1000 datas from a uniform distribution on [0,2] and plot the eCDF of this sample"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 36,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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+       "</svg>\n"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "using Plots  # for plots\n",
+    "N = 1000 # number of datas\n",
+    "u = 2*rand(N)   # uniform law on [0,2]\n",
+    "x_grid = -1:0.1:3\n",
+    "# Plot of the empirical cumulative distribution function\n",
+    "using Plots\n",
+    "F(x) = empirique(u,x)/N\n",
+    "p_uniform_cdf = plot(x_grid,F,xlabel=\"x\", ylabel=\"F(x)\", legend=false)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "3. Add on the plot the Cumulative Distribution Function\n",
+    "For thie use de Distributions Package"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 37,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# add the cumulative distribution function\n",
+    "using Distributions\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Distributions Package\n",
+    "\n",
+    "### Introduction\n",
+    "\n",
+    "There is lots of libraries (Packages in `julia`) : [https://julialang.org/packages/](https://julialang.org/packages/)\n",
+    "\n",
+    "For the documentation of the Distributions Package see \n",
+    "\n",
+    "[https://juliastats.org/Distributions.jl/stable/](https://juliastats.org/Distributions.jl/stable/)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 38,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "type de dist = Uniform{Float64}\n",
+      "mean(dist) = 1.0\n",
+      "median(dist) = 1.0\n",
+      "pdf(1.2) = 0.5\n",
+      "pdf(3) = 0.0\n",
+      "cdf(1.2) = 0.6\n",
+      "cdf(3) = 1.0\n",
+      "inverse of cdf(0.75) = 1.5\n"
+     ]
+    }
+   ],
+   "source": [
+    "using Distributions\n",
+    "using Plots\n",
+    "using LaTeXStrings\n",
+    "a = 0; b = 2;\n",
+    "dist = Uniform(a,b)  # dist is an object : the uniform distribution on [a,b]\n",
+    "println(\"type de dist = \",typeof(dist))\n",
+    "# you can acces to the mean or median of the distribution\n",
+    "println(\"mean(dist) = \", mean(dist))\n",
+    "println(\"median(dist) = \", median(dist))\n",
+    "# and the the PDF, CDF and inverse CDF function of the distribution\n",
+    "println(\"pdf(1.2) = \", pdf(dist,1.2))\n",
+    "println(\"pdf(3) = \", pdf(dist,3))\n",
+    "println(\"cdf(1.2) = \", cdf(dist,1.2))\n",
+    "println(\"cdf(3) = \", cdf(dist,3))\n",
+    "println(\"inverse of cdf(0.75) = \", quantile(dist,0.75))\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "#### Exercise 2\n",
+    "\n",
+    "Plot on the same first graph the CFD of the uniform distribution on [0,2]\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 39,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# to complete"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Triangular Distribution\n",
+    "We consider the distribution with the following density distribution\n",
+    "$$f(x) = \\begin{cases}\n",
+    "x\\quad\\textrm{pour}\\quad x\\in[0,1]\\\\\n",
+    "2-x\\quad\\textrm{pour}\\quad x\\in[1,2]\\\\\n",
+    "0\\quad\\textrm{sinon}\n",
+    "\\end{cases}$$\n",
+    "\n",
+    "Plot the density, cumulative dendity and inverse cumulative function"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 40,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "type de dist = TriangularDist{Float64}\n",
+      "params(dist) = (0.0, 2.0, 1.0)\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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+       "</svg>\n"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "using Distributions\n",
+    "using Plots\n",
+    "using LaTeXStrings\n",
+    "a = 0; b = 2;\n",
+    "dist = TriangularDist(a,b,1)  # min = a; max = b; mode = 1\n",
+    "println(\"type de dist = \",typeof(dist))\n",
+    "println(\"params(dist) = \", params(dist))\n",
+    "\n",
+    "x_grid = -1:0.1:3\n",
+    "# Density function\n",
+    "p1 = plot(x_grid, x->pdf(dist,x), color = :blue, linewidth=2, xlabel=(L\"x\"), ylabel=(L\"f(x)\")) \n",
+    "# Cumulative density function\n",
+    "p2 = plot(a-1:0.01:b+1, x->cdf(dist,x), linewidth=2, xlabel=(L\"x\"), ylabel=(L\"F(x)\"))  \n",
+    "# Inverse cumulative density function\n",
+    "p3 = plot(0:0.01:1, x->quantile(dist,x), xlims=(0,1), ylims=(0,2), color = :green, linewidth=2, xlabel=(L\"u\"), ylabel=(L\"F^{-1}(u)\"))\n",
+    "plot(p1,p2,p3, layout=(1,3),legend = false,size = (1200,300), margin = 0.6Plots.cm)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "#### Histogram\n",
+    "Generate a sample of 100 datas from the triangular distribution and plot on the same graph the histogram of the simple and the PDF function"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 41,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# Sample of 100 datas\n",
+    "t = rand(dist,100)\n",
+    "histogram(t) \n",
+    "plot!(a-0.5:0.1:b+0.5, x->pdf.(dist,x), linewidth=2, xlabel=(L\"x\"), ylabel=(L\"f(x)\"))   "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "#### Question\n",
+    "What is the problem ?\n",
+    "\n",
+    "1. Use the normalize=true parameter in the histogram function for solving the problem\n",
+    "2. Execute for a sample of N = 10000 datas"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Example of discret distribution : the binomial distribution\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 42,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "n, p, N = 10, 0.2, 10^3\n",
+    "bDist = Binomial(n,p)\n",
+    "xgrid = 0:n\n",
+    "plot(xgrid,pdf.(bDist,xgrid), color=:orange, seriestype = :scatter)\n",
+    "plot!(xgrid,pdf.(bDist,xgrid), line = :stem, linewidth=2, color=:orange)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "#### "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Central limit theorem\n",
+    "\n",
+    "We are going to illustrate the central limit theorem : \n",
+    "\n",
+    "Suppose $X_1,X_2,\\ldots$ is a sequence of Independent and identically distributed random variables with $E(X_i)=\\mu$ and $Var(X_i)=\\sigma^2 < +\\infty$. Then, as $n$ approaches infinity, the random variables $\\sqrt{n}(\\bar{X}_n - \\mu)$ converge in distribution to a normal distribution $\\mathcal{N}(0,\\sigma^2)$\n",
+    "\n",
+    "\n",
+    "### Exercise\n",
+    "1. Choose a distribution law dist, compute its mean $\\mu$ and its variance $\\sigma^2$ and $N$ the number of sanple\n",
+    "2. For $n$ in (1,2,5,20)\n",
+    "    1. Generate N=10000 samples of lenght n from the dist distribution\n",
+    "    2. Compute the means of the $N$ samples and the $N$ values $\\sqrt{n}(\\bar{X}_n - \\mu)$\n",
+    "    3. Plot the histogram of these $N$ values and the normal distribution $\\mathcal{N}(0,\\sigma^2)$\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 43,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Uniform{Float64}(a=0.0, b=12.0)"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "dist = Uniform(0,12)\n",
+    "# To complete"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Julia 1.10.5",
+   "language": "julia",
+   "name": "julia-1.10"
+  },
+  "language_info": {
+   "file_extension": ".jl",
+   "mimetype": "application/julia",
+   "name": "julia",
+   "version": "1.10.5"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}