{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tema d'esame di Statistica e analisi dei dati\n",
    "\n",
    "## Prova scritta del 12 giugno 2024 -- Prof. Malchiodi\n",
    "\n",
    "Scrivete qui sotto i dati richiesti e riportateli anche su tutti i fogli protocollo che vi sono stati consegnati. Non potete tenere altri fogli bianchi rispetto a quelli che vi sono stati consegnati, né potete utilizzare calcolatrici portatili (avete a disposizione direttamente il computer!). Potete tenere sul banco, oltre alla penna, un libro e un quaderno di appunti per consultazione. Tutte le altre cose che avete con voi, __compresi telefoni e smartwatch__, devono essere appoggiate o appese lontano dai banchi, dove vi verrà indicato. Potete scegliere a quali domande rispondere scrivendo su carta e a quali scrivendo ed eseguendo codice, eventualmente arricchito da commenti o da celle di testo. A fine prova dovrete consegnare __tutti__ i fogli che vi sono stati dati, e inviare la versione digitale di questo notebook, contenente il vostro svolgimento, utilizzando il sito https://upload.di.unimi.it.\n",
    "\n",
    "__Cognome e nome__\n",
    "\n",
    "__Matricola__"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Esercizio 1\n",
    "\n",
    "In questo esercizio considereremo la funzione\n",
    "\n",
    "$$ f(x) = \\frac{6}{a^3} \\left( a x - x^2 \\right) \\mathbb I_{[0, a]}(x), $$\n",
    "\n",
    "dove $\\mathbb I_A$ denota la funzione indicatrice dell'insieme $A$ e $a > 0$ è un parametro della funzione. Indicheremo inoltre con $X$ una variabile aleatoria avente $f$ come funzione di densità di probabilità, per un valore ignoto di $a$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__1.__ Dimostrate che $f$ è una funzione di densità di probabilità per ogni valore reale $a > 0$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__2.__ Calcolate il valore atteso di $X$, esprimendolo in funzione di $a$ (suggerimento: ragionando su alcune proprietà geometriche, potete giustificare il risultato senza fare conti)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__3.__ Indichiamo con $F$ la funzione di ripartizione di $X$. Ricavate la forma analitica di $F(x)$, esprimendola in funzione di $x$ e $a$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__4.__ Supponete, __solo in questo punto__, che $a = \\frac{1}{2}$. Scrivete ed eseguite del codice che disegni il grafico della funzione $F$ definita al punto precedente."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "def f(x, a):\n",
    "    return 6 / a**3 * (a * x - x**2) if 0 <= x <= a else 0\n",
    "\n",
    "def F(x, a):\n",
    "    return 6 / a**3 * (a * x**2 / 2 - x**3 /3) if 0 <= x <= a else 0 if x < 0 else 1\n",
    "\n",
    "x = np.linspace(-0.5, 1, 100)\n",
    "y = [F(i, 0.5) for i in x]\n",
    "\n",
    "plt.plot(x, y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__5.__ Il grafico che avete ottenuto al punto 4 potrebbe suggerire che $X$ segue una distribuzione normale? Perché? Validate o refutate questa ipotesi."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__6.__ Calcolate la varianza di $X$, esprimendola in funzione di $a$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Esercizio 2 ##\n",
    "\n",
    "In questo esercizio considereremo una popolazione $X$ la cui distribuzione è la stessa dell'omonima variabile aleatoria introdotta nell'esercizio precedente, dove $a$ rappresenterà un parametro incognito. Per $n \\in \\mathbb N$ fissato, $X_1, \\dots, X_n$ indicheranno delle variabili aleatorie che descrivono un campione estratto da $X$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__1.__ Dimostrate che la media campionaria è uno stimatore __distorto__ per il parametro $a$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__2.__ Calcolate il bias e lo scarto quadratico medio di $\\overline X$ rispetto ad $a$, esprimendoli __solo__ in funzione di $n$ e $a$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__3.__ La media campionaria gode della proprietà di consistenza in media quadratica se la utilizziamo per stimare $a$? Motivate la vostra risposta."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__4.__ Dovendo scegliere se applicare il metodo plug-in o il metodo della massima verosimiglianza per ottenere uno stimatore non distorto per $a$, quale opzione risulta più agevole? Perché?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__5.__ Applicate il metodo scelto al punto precedente e determinate uno stimatore $T$ che sia non distorto per $a$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__6.__ Utilizzando il teorema centrale del limite, determinate la distribuzione approssimata dello stimatore $T$ che avete ottenuto al punto 5."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__7.__ Calcolate la probabilità dell'evento che si verifica quando l'errore (in valore assoluto) che si compie usando $T$ per stimare $a$ sia minore o uguale di $1$, esprimendola in funzione di $a$, $n$ e della funzione di ripartizione della distribuzione normale standard, giustificando i vostri passaggi e indicando eventuali approssimazioni che è necessario introdurre."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Esercizio 3 ##\n",
    "\n",
    "Collegatevi al sito [upload.di.unimi.it](http://upload.di.unimi.it), selezionate l'esame di _Statistica e analisi dei dati_ per l'appello odierno e scaricate il file `risultati.csv`. Questo file contiene le seguenti informazioni raccolte da un ipotetico centro di formazione relativamente ai risultati che i propri studenti e le proprie studentesse hanno ottenuto nella tornata annuale di un test di idoneità organizzato a livello nazionale da un Ministero.\n",
    "\n",
    "- _matricola_: numero di matricola;\n",
    "- _genere_: genere (codificato come `'F'` oppure `'M'`);\n",
    "- _eta_: età;\n",
    "- _punteggio_: punteggio conseguito al test;\n",
    "- _tempo_: tempo necessario per terminare il test, espresso in minuti.\n",
    "\n",
    "In questo file il carattere `,` separa le colonne.\n",
    "\n",
    "__1.__ Scrivete ed eseguite del codice che visualizzi su righe differenti il nome di ogni attributo unitamente al corrispondente numero di valori mancanti."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>matricola</th>\n",
       "      <th>genere</th>\n",
       "      <th>eta</th>\n",
       "      <th>punteggio</th>\n",
       "      <th>tempo</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>4302229</td>\n",
       "      <td>F</td>\n",
       "      <td>20</td>\n",
       "      <td>20.49</td>\n",
       "      <td>24</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3199114</td>\n",
       "      <td>F</td>\n",
       "      <td>21</td>\n",
       "      <td>8.53</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>8399478</td>\n",
       "      <td>F</td>\n",
       "      <td>31</td>\n",
       "      <td>5.28</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2658176</td>\n",
       "      <td>F</td>\n",
       "      <td>35</td>\n",
       "      <td>17.37</td>\n",
       "      <td>21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1492848</td>\n",
       "      <td>M</td>\n",
       "      <td>35</td>\n",
       "      <td>23.34</td>\n",
       "      <td>22</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   matricola genere  eta  punteggio  tempo\n",
       "0    4302229      F   20      20.49     24\n",
       "1    3199114      F   21       8.53      9\n",
       "2    8399478      F   31       5.28      9\n",
       "3    2658176      F   35      17.37     21\n",
       "4    1492848      M   35      23.34     22"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "dati = pd.read_csv('risultati.csv')\n",
    "dati.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__2.__ Di che tipo è l'attributo _genere_? Sulla base della risposta data, visualizzate la distribuzione di questo attributo fornendo sia una formulazione tabulare, sia un grafico, motivando le vostre scelte."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "genere\n",
       "F    420\n",
       "M    369\n",
       "Name: count, dtype: int64"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dati['genere'].value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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OEVWUzHGsdOGrCgD21dkV1Lvl7rr7n5I5jv8wHwMgxlaXuuvFLSVzDJX1bdpe22I6BgCPWUXJeMOa7RxOBiD2Nlc16kBLp+kYUUPJHMMHLt3iAYC9hULShy56/qFkjoGSAWDK+t3uuXWCkjmKpna/tu1tMh0DgEe56UhmSuYoNu5ukEt33QbgABt2N7hmHzNK5ijWuWioCsB5Gtr8Kt/njtWtlMxRbNjVYDoCAI9zyyUzSuYoNu6hZACYtZ6Scafmji6OWgZgnFte7FIy3ZTWNJuOAAAqc8mOI5RMNyUsXQZgAw1tftU2dZiO0WeUTDeMZADYhRuejyiZbkpc8EMF4A5ltc5/PqJkuimp4XIZAHtgJOMybZ0B7aljZRkAe2Ak4zI7D7SynQwA23DDmVaUzCEqGxjFALCPqoY2dQWCpmP0CSVziOqGdtMRAOCgYEiqcfgy5ohKZtasWaqvP3LLg8bGRs2aNSsauYyoomQA2Ex1o7OflyIqmTfeeEOdnUceD9re3q6VK1dGI5cRVWwnA8Bm9jr8xW9Cb/7whg0bDn68efNmVVdXH/w8EAjo1Vdf1UknnRTdhDHk9FcMANxnr8Ofl3pVMpMmTZLP55PP5zvqZbHU1FQtWrQomvliqpKRDACbqW509pxMr0qmvLxcoVBII0aM0Lvvvqu8vLyDX0tKSlJ+fr7i4+OtyBkTex3+wwTgPp4ayQwbNkySFAw6e0nd0fgDQTV3dJmOAQCH8VTJHKqkpEQrVqxQTU3NEaVz9913RyNbTDW1UzAA7Kex3W86Qp9EVDKPPvqobrzxRuXm5mrQoEHy+XwHv+bz+RxaMs7+QQJwp5aOgOkIfRJRyfzkJz/Rfffdp4ULF0Y/kSGMZADYkdOfmyK6T6aurk5z586NfhqDnD4kBeBOLQ6fK46oZObOnavXX389+mkMcvqrBQDu1OYPKODgnXsjulw2atQo/fCHP9SaNWs0YcIEJSYmHvb1m266KVr5YoaSAWBXzR1dyk5N7MGftB9fKBTqdUUOHz782P9Cn0/bt2/va66YW/L2Dt39QpHpGABwhLe+N0tD+qWajhGRiEYy5eXl0U9iWFfAucNRAO7W2uncFWZs9f8RKgaAXQV7f8HJNiIaySxYsOC4X1+8eHGkeYyJ4KohAMSE50qmrq7usM/9fr82bdqk+vp6x54n4+QfIgB389zqsueff/6Ix4LBoG688UaNHDkyGrlijo5BX6QnBHRJbq3Oydit01SmvI4KxQVZsYjoiItbLCnbdIyIRLx3WXdxcXG69dZbde655+rOO++M1r82Zhz8QgExlhwX1Pk5B3R+1m6dHrddBW1blXKgWL56v3TkgbFA3/mcO/EftZKRpLKyMnV1OfPVW4ipfxyFzxfSzP71urBfpabEb9fQ9mKl122Rr6lNajKdDp4RF9Wn6piKKPmtt9562OehUEhVVVV6+eWX9dWvfjVa2WIq/pBNPuFdU7ObNLt/paYmlmt45zZl1RfJ19oktZpOBk+Lc+45XRGVzNq1aw/7PC4uTnl5ebr//vtPuPLMrtKSnPtDRGTGZrRqTk6Vzkqq0Kiubepfv1lxbfuk6h78w0Asea1kVqxYEf0khqUlOXc4ihMrSOnQZXlVmpayS2MCJcptLFJ8c5W013QyoAe8drnsY7W1tSouLpYkjRkz5rDjmJ0mPdm5rxRwuLwkvy7JrdHZaTt1qso0sGmzEht2SLWmkwER8lrJtLS06Lvf/a6WLFly8FTM+Ph4XXfddVq0aJHS0tKindNyjGScqfvS4cEtW5RUXyrfgaB0wHQ6IEqSMkwniFjEE/9vvvmmXnzxRU2fPl2StGrVKt1000267bbb9NBDD0U7p+UYydjfx0uHZ2Xu1sT4chW0bWHpMNwvMV1Kdm7JRLQLc25urp599lmde+65hz2+YsUKfelLX1JtrfOuS2ypatTFv1lpOgY+4vOFNHNAvS7MrtTk+O0a1rFN6Qc2y9fVZjoaEFv9h0s3rzOdImIRjWRaW1s1cODAIx7Pz89Xa6sz13pmJHO5zKQzspo0e0Clpibt0IiO4vDS4ZYmqcV0MsCwjHzTCfokomfWadOm6Z577tGSJUuUkpIiSWpra9OPfvQjTZs2LdoZY6J/epLpCJ5x+NLhEvWvL2LpMHAsXiyZX//615o9e7YKCgo0ceJESdL69euVnJzs2GOZM5ITlJYU7+hzG+wovHS4WtNSdrJ0GIhExpFXjZwkopKZMGGCSkpK9NRTT2nr1q2SpKuvvlrXXHONUlOdeXqbJOVnJmvHfmde7rODT5YO79KpKmXpMBANXiyZn/70pxo4cKCuv/76wx5fvHixamtrtXDhwmjli6n8zBRKpofSEwK6OHefzs3Y9dHS4a1Kqi9h6TAQbenOvf9QkZbM73//ez399NNHPD5+/HhdddVVji2ZvKxk0xFsKTkuqFk5B3R+5h5NjN+ugtYtSqlj6TAQE14cyVRXV2vw4MFHPJ6Xl6eqqqpo5DJiYGaK6QjGHXPpMLsOA2Z4sWQKCwu1evVqDR8+/LDHV69erSFDhkQrW8zle3AkMyW7SRf3P3Tp8Gb5WhpZOgzYhRdXl11//fW65ZZb5Pf7Dx63/O9//1t33nmnbrvttmhnjJlBWe4eyYzNaNUlA6r0qeSdH+06zNJhwPa8WDJ33HGH9u/fr29961vq7OyUJKWkpGjhwoW66667op0xZoblOG/PtWM5dOnwKYFS5TUWKb65UqoxnQxAj6VkSwnOvsIS0bYyH2tubtaWLVuUmpqq0aNHKznZ2d+Mhja/Jv7Ieff55CT5denRlg4DcLa8sdK33zGdok/6tJdKRkaGzjzzzOilMSw7NVG5GUna19xpOsoxfbx0+Jz0XTrNt11DWrawdBhwq7yxphP0GRt2dTMiN0P7mu3xbJ0YF9IFOft1fuYenR6/XQVtW5VaVyxffSdLhwEvGHSa6QR9Rsl0Mzw3Xe/uiH3JfLx0+IKsPZqSsEPDOopZOgx43aDTTSfoM0qmmxF56TH57xxcOpy4Q8P925RdV8TSYQCHGzTBdII+o2S6GZEX/cOBTklv05ycKn06uYKlwwB6Ji1XynLufYcfo2S6OWVg30qmIKVDl+ZWa1rqTo1h6TCASLlgPkaUzJGGDkhTZkqCmtq7Tvhnc5L8mpNbqxlpO3VqqFQDm7cosaFc2heTqADcbCAl40o+n0/jh2RpzfbDJ//TEwK6OKdW52Tu0WkqY+kwAGu5YNJflMzRTS7IUv+mbUcuHW7olBpMpwPgCS6Y9Bclc3QLhxZL797E0mEAZiSkSLmnmE4RFXGmA9hSgXt2MQDgQHljpXh3jAEomaPpVyhlHnleDgDEhEtWlomSOQ5GMwBMccmkvyiZ4yg8y3QCAF417DOmE0QNJXMsjGQAmJAxyDUry0TJHMfgSVK8s8/HAeBAoy4wnSCqKJljSUyRTp5uOgUArxl1vukEUUXJHM+YS0wnAOAlvnhp5HmmU0QVJXM8Yy42nQCAlxRMlVL7m04RVZTM8WQXuGoCDoDNjbrQdIKoo2ROhEtmAGLFZfMxomR6gEtmAGIhPU8aMtl0iqijZE5kyGQp0/mn0wGwuZGzJJ/PdIqoo2R6Ysxs0wkAuJ0L52NEyfQQ8zIArOSLC49kXIiS6YnhM6WkDNMpALjVkMlSeo7pFJagZHoiIdl1N0gBsJHxXzCdwDKUTE9xyQyAFeISpYlXmU5hGUqmp0ZfFN7yAQCiacxsKT3XdArLUDI9lZ7DPTMAom/ytaYTWIqS6Y2pC0wnAOAmmYNdt7V/d5RMb4ycJfUfbjoFALeYeLUU5+7L8JRMb/h80tSvmU4BwC0mzzOdwHKUTG9NmseJmQD6bth0KWek6RSWo2R6Kz1HGvc50ykAOJ0HRjGiZCLEAgAAfZGcJY27wnSKmKBkIjFsmpQ/znQKAE41/vNSUprpFDFByUSK0QyASE25znSCmKFkInX6l6XEdNMpADhN/nipYKrpFDFDyUQqJUuacKXpFACcZsatphPEFCXTF2f+l+kEAJwkd4yrd1w+GkqmLwZPDK91B4CemHm7FOetp11v/d9aYdYPTCcA4AQ5o6TTvmg6RcxRMn017DPSyPNNpwBgdzNud/0+ZUdDyUQDoxkAx9N/uHT6l0ynMIKSiYaTpkhjLzWdAoBdzfTmKEaUTBTN+oHk49sJoJt+w6TT3Xu88onwrBgt+adKp3HfDIBuZtwqxSeYTmEMJRNN590lxXn3lwlAN9lDpUnXmE5hFCUTTQNGeP4XCsAhzr5Fik80ncIoSibazrmTQ80ASNmF0uRrTacwjpKJtuwCdmgGIF30f6WEJNMpjKNkrDDjNnZoBrxs9EXSuMtNp7AFSsYKGXnS9JtNpwBgQkKqdMnPTaewDUrGKmf/t5Q31nQKALE283ap/8mmU9gGJWOVhCTp8kXcoAl4Se4p0mduMp3CVngGtFLhWdJUzpwBPGPO/Uz2d0PJWO2Ce6SsAtMpAFjt9C9Lw2eaTmE7lIzVkjOlS39pOgUAK6VkS5+9z3QKW6JkYuGUizx5WBHgGeffHV5ViiNQMrFy8c+l1AGmUwCItiFTpDO4AftYKJlYSc+VLmI4DbiKL1669FdSHE+lx8J3JpYmfUUacZ7pFACi5TPflYZMMp3C1iiZWLvs11JimukUAPqq8NPSrB+aTmF7lEys9T+ZX0zA6VIHSFc+5unDyHqKkjFh2reksZeaTgEgIj7p8w+Hd1zHCVEyplzxkDRgpOkUAHrrM98J35aAHqFkTEnJkr78JPMzgJMUnCWdf6/pFI5CyZg0cJx02QOmUwDoidT+0pWLmYfpJUrGtNPnSmd903QKACdyxUNSv0LTKRyHkrGDi+6TCj9lOgWAY5n2HWnMxaZTOBIlYwfxidLcP0np+aaTAOjupKnSBczDRIqSsYusweHrvb5400kAfCylnzT38fALQUSEkrGT4TPC588AMC8uIXzDZb+hppM4GiVjN9Nvlk693HQKAJf+Shp1gekUjkfJ2NEVv5MGnW46BeBdM++QplxnOoUrUDJ2lJwpXfu8lDPadBLAeyZeLc36gekUrkHJ2FV6rnTd36Rs1uUDMTN8pnT5ItMpXIWSsbPsAum6F6R0jnUFLDdwQnirJ1aSRRUlY3c5I8OXzlKyTScB3GsAf8+sQsk4waAJ0lf+KiWmm04CuE/WSeErBhlcMbACJeMUQz8lXfWkFJ9kOgngHmk50rV/Y08yC1EyTjJylvTFx9gVAIiG5Cxp3nNS3immk7gaJeM04y7/aPWLz3QSwLmSs6Wv/EUaMtl0EtejZJxo8jXS7J+ZTgE4U3q+NP8ladg000k8gdN3nOrTN0ihgPTa/0gKmU4DOEO/YR/d6MzR57HiC4VCPEM52abnpOdvlAIdppMA9pY/Xrp2mZQ5yHQST6Fk3GDHKmnpV6T2BtNJAHsq/LT0laXhI5QRU5SMW9RskZ78otS4x3QSwF5GfzZ8KGBSmukknkTJuEljpfTklVJNkekkgD1M+JJ0xUNSPNPPplAybtPeIC29Rtqx0nQSwKyzvild/L+Sj+X+JlEybtTVKf3tRmnTs6aTAGac9z/SOXeaTgFKxsVCIemfd0tvPWA6CRA7cYnSJT+Xpi4wnQQfoWTcbs3D0mt3SaGg6SSAtbILpbl/lAqmmk6CQ1AyXlD8D+n5b7LEGe416kLpC49IaQNMJ0E3lIxX1O2Q/jpfqlxrOgkQPb546by7pBm3M8FvU5SMl3R1Sq99X3rvUdNJgL5Lz5eufCx8ZDJsi5Lxok3LpL/fJHU2mU4CRGbYdOnKxWwR4wCUjFftL5OeXSBVrTOdBOgFnzT9Zun8u6U4zlVyAkrGywJ+aflPwsucWX0Gu0vpJ33+YWnMxaaToBcoGUjlK8Orz9j3DHZ10hnSlY9L/YeZToJeomQQ1lYnvXiLtPlvppMAn0jKkGb9QDrrG1wecyhKBodb/4z0+v9ILbWmk8DrxsyRLvmFlH2S6SToA0oGR2pvCM/VvPdY+PRNIJYyh4S3hjn1MtNJEAWUDI6teqP08u3SrjWmk8ALfHHSmddL5/9QSs40nQZRQsng+EIhad3T0r/u4RIarDNognTZb8IT/HAVSgY901YvrbiPS2iIrsQ06dy7pE9/i4PFXIqSQe9UbZBeuV3a9Y7pJHC60Z+V5twv9RtqOgksRMmg97iEhr4YOi08ehlxjukkiAFKBpFrq5dW/VJ6bzH7oOHECs6Uzvu+NHKW6SSIIUoGfddWJ73ze+mdh8MfA4caMiVcLqMvNJ0EBlAyiJ6OZun9x6S3fiu11JhOA9MGT5TO/b40ZrbpJDCIkkH0+dulD5dIq38jNe42nQaxNnBC+CCxsXNMJ4ENUDKwTsAvrV8qrfqVdKDMdBpYLX+cdO73pFMv55RKHETJwHrBgFT0vLTyfqlms+k0iKa4RGnsJdKUr4Yn9CkXdEPJIHZCIankn9K6J6XiV6VAh+lEiNSAEeFimXSNlJFnOg1sjJKBGa0HpE3Phe+3qfzQdBr0RHxSeNPKKV+Vhs9k1IIeoWRgXm2xtO4pacNfpKYq02nQXe4p4WKZeLWUnmM6DRyGkoF9BAPS9hXh0c3Wl6WudtOJvCshRRr3OemM+dKwz5hOAwejZGBP7Q3SpmXS+j+zT1qspOeH9xM75bPSiPOklCzTieAClAzsr7EqPMIpWyFtf4MbPaPGJw2ZJI2+KFwsQ6Ywz4Koo2TgLKFQ+DC17SuksuXSzjVcVuuNpExp5LnhYhn9WSlzoOlEcDlKBs7mb5Mq3goXTtkKqabIdCKb8Um5o6VRF4RLZdh0KSHJdCh4CCUDd2naGx7l7FwTvvGzZovU0Wg6VWz44sIrwQZP/ORt0OnMrcAoSgbuV79T2rs5PMrZWxT+eH+JFOwynSxycQlS3lhp8KRDCmWClJRmOhlwGEoG3tTVKe3bFh7t7C0Kv68tDh/C5m81ne4jPikjX8ou+OitUMoZGS6U/PFSYorpgMAJUTJAd52t4bJp3Se17D/k44/eun/c1RG+VBUXH37v+/i975DHDn08LnyefeqAcImk50rpeZ+8fVwsWQXMn8DxKBkAgGXiTAcAALgXJQMAsAwlAwCwDCUDALAMJQMAsAwlAwCwDCUDALAMJQMAsAwlA9jY/Pnz5fP5dMMNNxzxtW9/+9vy+XyaP3++kWxAT1AygM0VFhZq6dKlamtrO/hYe3u7nn76aQ0dOtRoNuBEKBnA5qZMmaLCwkItW7bs4GPLli3T0KFDNXnyZKPZgBOhZAAHWLBggR5//PGDny9evFhf+9rXjGYCeoKSARxg3rx5WrVqlSoqKlRRUaHVq1dr3rx5pmMBJ5RgOgCAE8vLy9OcOXP0xz/+UaFQSHPmzFFubq7pWMAJUTKAQyxYsEDf+c53JEkPPvig6ThAj1AygEPMnj1bnZ2d8vl8uuiii0zHAXqEkgEcIj4+Xlu2bDn4MeAElAzgIFlZWaYjAL3C8csAAMuwhBkAYBlKBgBgGUoGAGAZSgYAYBlKBgBgGUoGAGAZSgYAYBlKBgBgGUoGAGAZSgYAYBlKBgBgGUoGAGAZSgYAYBlKBgBgGUoGAGAZSgYAYBlKBgBgGUoGAGAZSgYAYBlKBgBgGUoGAGAZSgYAYBlKBgBgGUoGAGAZSgYAYBlKBgBgGUoGAGCZ/w+J0qnKw7fWUwAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dati['genere'].value_counts().plot.pie()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__3.__ Considerate l'attributo _punteggio_, e ripetete l'analisi svolta al punto precedente, valutando se debba essere fatta nello stesso modo oppure se debbano essere utilizzati strumenti diversi."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dati['punteggio'].plot.hist(bins=30, density=True)\n",
    "\n",
    "a = 36\n",
    "x = np.linspace(0, a, 100)\n",
    "y = [f(i, a) for i in x]\n",
    "plt.plot(x, y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__4.__ Valutate l'ipotesi che vi sia una relazione tra gli attributi _punteggio_ e _tempo_, specificando eventualmente il tipo e la forza della relazione determinata. Quali strumenti avete utilizzato per valutare questa ipotesi? Perché? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dati.plot.scatter('punteggio', 'tempo')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(0.9098656274110432)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dati['punteggio'].corr(dati['tempo'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__5.__ Gli esperti del centro di formazione sospettano che l'attributo _punteggio_ dovrebbe sia ben descritto da una distribuzione analoga a quella studiata nell'Esercizio 1. Scegliete uno strumento che ha senso utilizzare per validare questa ipotesi e applicatelo, commentando i risultati ottenuti."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Esercizio 4 ##\n",
    "\n",
    "I valori dell'attributo _punteggio_ nel dataset considerato al punto precedente sono espressi in una scala il cui valore massimo $a$ non è stato reso noto, e il centro di formazione vuole stimare questo valore.\n",
    "\n",
    "__1.__ Sulla base della soluzione che avete proposto per l'Esercizio 2, calcolate una stima per $a$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(35.95561470215463)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a_hat = dati['punteggio'].mean() * 2\n",
    "a_hat"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__2.__ Utilizzare il risultato dell'Esercizio 2.7 per stimare la probabilità che la stima ottenuta al punto precedente comporti un errore (in valore assoluto) minore o uguale di $1$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__3.__ Indichiamo con $X$ la variabile aleatoria che descrive il punteggio ottenuto. Il test si considera sostenuto con successo se si ottiene un punteggio superiore a 21. Calcolate la frequenza di questo evento nel dataset considerato e confrontatela con la probabilità $\\mathbb P(X > 21)$, calcolata sostituendo al parametro $a$ la corrispondente stima ottenuta nel punto 1 di questo esercizio, commentando i risultati ottenuti."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.385297845373891"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(dati['punteggio'] > 21) / len(dati)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(0.37510753028463784)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p = 1 - F(21, a_hat)\n",
    "p"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__4.__ Ipotizzando che sussista indipendenza tra i punteggi ottenuti nel test da persone diverse che lo sostengono, supponiamo che tre studenti o studentesse del centro svolgano il test in una stessa tornata, e indichiamo con $Y$ la variabile aleatoria che indica il numero di test superati. Dite quale distribuzione segue questa variabile aleatoria, e calcolate le seguenti probabilità, esprimendo anche l'evento corrispondente in termini di $Y$:\n",
    "\n",
    "a. tre persone svolgono il test nella stessa tornata, e tutte e tre lo superano;\n",
    "\n",
    "b. tre persone svolgono il test nella stessa tornata, ma solo una tra esse lo supera;\n",
    "\n",
    "c. tre persone svolgono il test nella stessa tornata, e al più una tra esse lo supera;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(np.float64(0.052779752348182316),\n",
       " np.float64(0.4394278922410175),\n",
       " np.float64(0.6834425268676432))"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import scipy.stats as st\n",
    "\n",
    "Y = st.binom(3, p)\n",
    "\n",
    "(Y.pmf(3), Y.pmf(1), Y.cdf(1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__5.__ Ipotizzando che sussista indipendenza tra punteggi ottenuti da una stessa persona in tempi diversi, indichiamo con $Z$ la variabile aleatoria che indica il numero di bocciature al test prima di superarlo. Dite quale distribuzione segue $Z$, e calcolate la probabilità dei seguenti eventi, esprimendo anche l'evento corrispondente in termini di $Z$:\n",
    "\n",
    "a. una persona supera il test al quarto tentativo;\n",
    "\n",
    "b. una persona che non ha superato il test al secondo tentativo deve svolgerlo nuovamente almeno due volte prima di superarlo."
   ]
  }
 ],
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