diff --git a/Lecture 9/Chi^2.ipynb b/Lecture 9/Chi^2.ipynb
index 8bc43b7..3b0dbea 100644
--- a/Lecture 9/Chi^2.ipynb	
+++ b/Lecture 9/Chi^2.ipynb	
@@ -1,333 +1,221 @@
 {
  "cells": [
   {
    "cell_type": "code",
    "execution_count": 1,
    "metadata": {},
    "outputs": [],
    "source": [
     "options(repr.plot.width=10, repr.plot.height=6.5)   # this command just formats the size of the figures. Adapt to view them nicely\n",
     "                                                    # in your browser."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 4,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "image/png": 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2677bb6/8PUtm3bd999t/qAX/3qV+tc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\n9913Xz2zb731VvWC8eP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N4GBSFAVRAeXt/dKVRe9pp5y5Ytu08w5qRZkixEtGHD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\n51T6SU0WCxG91r59IGug75K47ZbKN9ZX6+vLLPl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       "text/plain": [
        "Plot with title “Histogram of X1^2”"
       ]
      },
      "metadata": {
       "image/png": {
        "height": 390,
        "width": 600
       },
       "text/plain": {
        "height": 390,
        "width": 600
       }
      },
      "output_type": "display_data"
     },
     {
      "data": {
       "image/png": 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f0WLLBxrm6dlJZb06kMawAAAABQYRRC9UpKShr8/uAn+zypH/n2k2+P7DpS4hur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\nGup5UYTm9Ob8/PyMj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       "text/plain": [
        "Plot with title “Histogram of X1^2 + X2^2 + X3^2”"
       ]
      },
      "metadata": {
       "image/png": {
        "height": 390,
        "width": 600
       },
       "text/plain": {
        "height": 390,
        "width": 600
       }
      },
      "output_type": "display_data"
     }
    ],
    "source": [
     "# The chi^2 test\n",
     "\n",
     "# Visualized chi^2 distributions\n",
     "\n",
     "# chi_df^2 = sum(i=1..df) X_i^2. Sum the squares of df N(0,1) i.i.d. standard normal RVs. \n",
     "\n",
     "# work from the definition.\n",
     "\n",
     "X1 <- rnorm(10000,mean = 0,sd = 1) #generate 1000 random N(0,1) datapoints.\n",
     "hist1=hist(X1^2,breaks = seq(0,30,by=0.1),plot = FALSE) #chi^2_1\n",
     "plot( hist1, col=rgb(0,0,1,1/4),xlim=c(0,10), ylim=c(0,1000), xlab = \"chi^2\")\n",
     "\n",
     "X2 <- rnorm(10000,mean = 0,sd = 1) #generate 1000 random N(0,1) datapoints.\n",
     "hist2 <- hist(X1^2+X2^2,breaks = seq(0,30,by=0.1),plot = FALSE) #chi^2_2\n",
     "plot( hist2, col=rgb(1,0,0,1/4),  add=T) \n",
     "\n",
     "X3 <- rnorm(10000,mean = 0,sd = 1) #generate 1000 random N(0,1) datapoints.\n",
     "hist3 <- hist(X1^2+X2^2+X3^2,breaks = seq(0,30,by=0.1),plot = FALSE) #chi^2_3\n",
     "plot( hist3, col=rgb(0,1,0,1/4),  add=T)  \n",
     "\n",
     "\n",
     "# Use the numerical computation of chi^2 in R\n",
     "df=3 #degree of freedom = number of RV to square and sum\n",
     "\n",
     "x=seq(0,40,by=0.05)\n",
     "y=1000*dchisq(x,df)  #pdf of chi^2\n",
     "\n",
     "plot( hist3, col=rgb(0,1,0,1/4),xlim=c(0,15))  \n",
     "lines(x,y, xlab = \"chi^2\", ylab = \"probability density\", col='red')"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 16,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/html": [
        "<span style=white-space:pre-wrap>'measured chi^2:  6.8        critical chi^2:  11.0704976935164'</span>"
       ],
       "text/latex": [
        "'measured chi\\textasciicircum{}2:  6.8        critical chi\\textasciicircum{}2:  11.0704976935164'"
       ],
       "text/markdown": [
        "<span style=white-space:pre-wrap>'measured chi^2:  6.8        critical chi^2:  11.0704976935164'</span>"
       ],
       "text/plain": [
        "[1] \"measured chi^2:  6.8        critical chi^2:  11.0704976935164\""
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     },
     {
      "data": {
       "image/png": 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Y8WPdUP6XoPhchzwHFOV6U3SPNv8wuW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\n7liirocAAAAASUVORK5CYII=",
       "text/plain": [
        "Plot with title “Histogram of sample(1:6, n, replace = T, prob = probabilities)”"
       ]
      },
      "metadata": {
       "image/png": {
        "height": 390,
        "width": 600
       },
       "text/plain": {
        "height": 390,
        "width": 600
       }
      },
      "output_type": "display_data"
     }
    ],
    "source": [
     "# chi^2 testing\n",
     "\n",
     "# Example: The unfair dice\n",
     "\n",
     "# Generate some data for testing:\n",
     "n = 10  # number of dice throw\n",
     "\n",
     "# Probabilities : Vector of p_i. i-th number: probability to find i on dice\n",
     "#probabilities <- c(1/6,1/6,1/6,1/6,1/6,1/6)         # a fair die\n",
     "probabilities <- c(1/10,1/10,1/10,1/10,3/10,3/10)   # an unfair die, lots of 5 and 6\n",
     "\n",
     "mydata=hist(sample(1:6,n,replace=T,prob=probabilities), breaks = seq(0.5,6.5,by=1)) # role die n times, count observations.\n",
     "\n",
     "# 1) Hypothesis\n",
     "\n",
     "#H_1: This dice is unfair! H_0: the dice is fair. Under H_0, all p_i = 1/6.\n",
     "# Is there significant evidence that the observed numbers deviate from what we expect if H_0 was valid?\n",
     "\n",
     "# 2) Significance\n",
     "alpha=0.05\n",
     "\n",
     "# 3) Compute test statistic\n",
     "\n",
     "chisquare = 0\n",
     "\n",
     "for (i in seq(1,6,by=1)) { chisquare = chisquare +  (mydata$counts[i]-n*1/6)^2/(n*1/6)  }\n",
     "\n",
     "# 4) Critical region\n",
     "# Reject H_0 if chisquare > chi_5(1-alpha)\n",
     "\n",
     "K= qchisq(1-alpha,5)\n",
     "\n",
     "# 5) decide\n",
     "\n",
     "paste('measured chi^2: ',chisquare, '       critical chi^2: ',K )\n",
     "\n"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 15,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
        "\n",
        "\tChi-squared test for given probabilities\n",
        "\n",
        "data:  mydata$counts\n",
        "X-squared = 45.8, df = 5, p-value = 9.975e-09\n"
       ]
      },
      "metadata": {},
      "output_type": "display_data"
     }
    ],
    "source": [
     "# Repeat in R\n",
     "\n",
     "chisq.test(x=mydata$counts,p = c(1/6,1/6,1/6,1/6,1/6,1/6))"
    ]
   },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
-       "0.158654967279885"
-      ],
-      "text/latex": [
-       "0.158654967279885"
-      ],
-      "text/markdown": [
-       "0.158654967279885"
-      ],
-      "text/plain": [
-       "[1] 0.158655"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "pnorm(2/3,mean=1,sd=1/3)-pnorm(-2/3,mean=1,sd=1/3)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
-       "0.158654967279885"
-      ],
-      "text/latex": [
-       "0.158654967279885"
-      ],
-      "text/markdown": [
-       "0.158654967279885"
-      ],
-      "text/plain": [
-       "[1] 0.158655"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "pnorm(2-3)-pnorm(-2-3)"
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-  },
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