{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tema d'esame di Statistica e analisi dei dati\n",
    "\n",
    "## Prova scritta del 22 giugno 2023 -- 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 supporremo che la password per accedere a un sito di home banking sia composta da cinque\n",
    "cifre decimali, e indicheremo con $p$ una prefissata password.\n",
    "\n",
    "__1.__ Calcolate il numero di password distinte."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "__2.__ Calcolate la probabilità che una password estratta uniformemente a\n",
    "caso tra tutte quelle possibili sia uguale a $p$.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "__3.__ Calcolate il numero di password distinte che contengono una\n",
    "stessa cifra ripetuta nelle prime tre posizioni.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "__4.__ Calcolate la probabilità del punto 1., condizionandola al fatto che\n",
    "le cifre nelle prime tre posizioni in $p$ sono tutte uguali e scegliendo la password uniformemente a caso tra tutte quelle che hanno le prime tre cifre uguali.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__5.__ Calcolate il numero di password distinte che contengono una\n",
    "stessa cifra ripetuta in tre posizioni consecutive."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__6.__ Calcolate la probabilità analoga a quella del punto 4, rimuovendo la richiesta che il blocco di tre cifre uguali si trovi all'inizio della password."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Esercizio 2\n",
    "\n",
    "Sia $X \\sim \\mathrm G(h)$ una variabile aleatoria distribuita secondo un modello geometrico di parametro $h$.\n",
    "\n",
    "__1.__ Quali sono i valori $x$ per i quali ha senso calcolare la probabilità $\\mathbb P(X > x)$?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__2.__ Per un generico $x \\in \\mathbb N$, calcolate la probabilità\n",
    "$\\mathbb P(X > x)$, esprimendola in funzione del parametro $h$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__3.__ Esprimete in funzione di $x$ e $h$ il valore $F_X(x)$ restituito dalla funzione di ripartizione di $X$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__4.__ Disegnate il grafico della fuzione $F_X$ ottenuta al punto precedente, fissando $h = \\frac{4}{10}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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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, h):\n",
    "    return 1 - ( 1 - h ) ** (np.floor(x) + 1)\n",
    "\n",
    "x = np.linspace(0, 15)\n",
    "y = F(x, 4/10)\n",
    "\n",
    "plt.step(x, y)\n",
    "plt.ylim(0, 1)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Esercizio 3 ##\n",
    "\n",
    "Per $n \\in \\mathbb N$ fissato, siano $X_1, \\dots, X_n$ delle variabili aleatorie indipendenti e identicamente distribuite secondo un modello geometrico di parametro $h$. Nel resto dell'esercizio considereremo queste variabili come un campione estratto da una popolazione la cui distribuzione è la stessa della variabile aleatoria $X$ descritta nell'Esercizio 2 e supporremo $\\mu = \\mathbb E(X)$ e $T = \\frac{1}{n} \\sum_{i=1}^n X_i$.\n",
    "\n",
    "__1.__ La variabile aleatoria $T$ è uno stimatore non distorto per $\\mu$? Giustificate la vostra risposta."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__2.__ La variabile aleatoria $T$ descritta al punto precedente è uno stimatore non distorto per $h$? Giustificate la vostra risposta."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__3.__ Calcolate il bias e lo scarto quadrato dello stimatore $T$, __con riferimento alla stima del parametro $h$__."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__4.__ Lo stimatore $T$ gode della proprietà di consistenza in media quadratica\n",
    "__relativamente alla stima del parametro $h$__? Giustificate la vostra risposta."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__5.__ Fissato $\\epsilon > 0$, esprimete in funzione di $\\epsilon$, $h$ e $n$ la probabilità dell'evento che si verifica quando l'errore (in valore assoluto) che si compie usando $T$ per stimare $\\mu$ sia minore o uguale a $\\epsilon$, giustificando i vostri passaggi e indicando eventuali approssimazioni che è necessario introdurre."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__6.__ Proponete uno stimatore $S$ per $h$, giustificando la scelta fatta."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Esercizio 4 ##\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 `banking.csv`. Questo file contiene le seguenti informazioni raccolte da un'ipotetica banca relativamente agli accessi al proprio sito di home banking:\n",
    "\n",
    "- _utente_: codice univoco che identifica un utente;\n",
    "- _tentativi_: numero di tentativi successivi di accedere al sito di home banking prima di riuscire ad autenticarsi;\n",
    "- _minuti_: ora di accesso, indicata come numero di minuti passati dalla mezzanotte;\n",
    "- _illecito_: valore binario che vale $1$ se l'accesso al sito di home banking è stato denunciato come illecito da parte del legittimo proprietario del conto, e $0$ altrimenti.\n",
    "\n",
    "In questo file il carattere `,` separa le colonne.\n",
    "\n",
    "__1.__ Scrivete ed eseguite del codice che vi permetta di capire quanti utenti distinti sono contenuti nel _dataset_, nonché quali siano gli attributi per i quali vi sono dei 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>utente</th>\n",
       "      <th>tentativi</th>\n",
       "      <th>minuti</th>\n",
       "      <th>illecito</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>342760</td>\n",
       "      <td>1.0</td>\n",
       "      <td>154</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>895078</td>\n",
       "      <td>1.0</td>\n",
       "      <td>154</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>36509</td>\n",
       "      <td>1.0</td>\n",
       "      <td>210</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>182008</td>\n",
       "      <td>1.0</td>\n",
       "      <td>973</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>961138</td>\n",
       "      <td>2.0</td>\n",
       "      <td>176</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   utente  tentativi  minuti  illecito\n",
       "0  342760        1.0     154         0\n",
       "1  895078        1.0     154         0\n",
       "2   36509        1.0     210         0\n",
       "3  182008        1.0     973         1\n",
       "4  961138        2.0     176         0"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "dati = pd.read_csv('banking.csv')\n",
    "dati.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1752"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dati['utente'].nunique()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "colonna utente, 0 casi mancanti\n",
      "colonna tentativi, 7 casi mancanti\n",
      "colonna minuti, 0 casi mancanti\n",
      "colonna illecito, 0 casi mancanti\n"
     ]
    }
   ],
   "source": [
    "for c in dati:\n",
    "    print(f'colonna {c}, {sum(dati[c].isnull())} casi mancanti')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from statsmodels.api import qqplot\n",
    "\n",
    "qqplot(dati['minuti'], fit=True, line='45')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__2.__ Valutate l'ipotesi che i valori dell'attributo _minuti_ possano essere assimilati a un campione estratto da una popolazione distribuita secondo un modello normale, spiegando il vostro ragionamento."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__3.__ Visualizzate graficamente l'attributo _minuti_, motivando il tipo di visualizzazione che avete scelto e commentate il risultato ottenuto anche alla luce di quanto emerso al punto precedente."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dati['minuti'].plot.hist(bins=100)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__4.__ Valutate l'ipotesi che vi sia una relazione tra gli attributi _minuti_ e _illecito_, specificando eventualmente di che tipo è la relazione determinata. Quali strumenti avete utilizzato per valutare questa ipotesi? Perché? "
   ]
  },
  {
   "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.plot.scatter('minuti', 'illecito')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9478451073104909\n"
     ]
    }
   ],
   "source": [
    "print(dati['minuti'].corr(dati['illecito']))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__5.__ Descrivete l'attributo _tentativi_ utilizzando la rappresentazione grafica che ritenete più adeguata, motivando la scelta fatta e commentando i risultati ottenuti."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "freq = dati['tentativi'].value_counts(normalize=True)\n",
    "plt.vlines(freq.index, 0, freq.values)\n",
    " #plt.plot(freq.index, freq.values, 'o')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__6.__ I risultati ottenuti ai punti precedenti dovrebbero suggerire l'esistenza di due diverse tipologie di accessi al sito di home banking, discriminate dal valore dell'attributo _illecito_. Memorizzate in una variabile `dati_illeciti` tutti i casi del dataset che si riferiscono agli accessi di tipo illecito, e visualizzate graficamente la distribuzione dei corrispondenti valori dell'attributo _tentativi_."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dati_illeciti = dati[dati['illecito'] == 1]\n",
    "\n",
    "freq = dati_illeciti['tentativi'].value_counts(normalize=True)\n",
    "plt.vlines(freq.index, 0, freq.values)\n",
    " #plt.plot(freq.index, freq.values, 'o')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__7.__ Sulla base dei risultati ottenuti nel punto precedente, considerate separatamente ognuno dei seguenti modelli di distribuzione, specificando se (e perché) si tratta di modelli ragionevoli per i valori memorizzati nella variabile `dati_illeciti`:\n",
    "\n",
    "- il modello esponenziale,\n",
    "- il modello gaussiano,\n",
    "- il modello geometrico,\n",
    "- il modello uniforme discreto."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Esercizio 5 ##\n",
    "\n",
    "In questo esercizio ci concentreremo sui valori dell'attributo _tentativi_ relativi __ai soli accessi illeciti__ al sito di home banking, e li interpreteremo come i valori assunti da un campione estratto da una popolazione distribuita come una variabile aleatoria $Y$.\n",
    "\n",
    "__1.__ Ci sono valori mancanti per l'attributo in questione? Se sì, quanti sono?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7\n"
     ]
    }
   ],
   "source": [
    "num_na = (dati_illeciti['tentativi'].isnull().sum())\n",
    "print(num_na)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__2.__ Stimate il valore atteso $\\mathbb E(Y)$, specificando la dimensione del campione utilizzato e indicando eventuali proprietà dello stimatore utilizzato."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.5055733988286417\n"
     ]
    }
   ],
   "source": [
    "print(dati_illeciti['tentativi'].mean())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5293\n"
     ]
    }
   ],
   "source": [
    "print(len(dati_illeciti) - num_na)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__3.__ I dati a disposizione permettono di garantire, con probabilità maggiore o uguale a 0.99, che la stima fatta al punto precedente comporti un errore (in valore assoluto) grande al più $\\epsilon = 0.1$?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.stats as st\n",
    "\n",
    "Z = st.norm()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(0.0)"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Z.ppf(0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2619.4909775321353\n"
     ]
    }
   ],
   "source": [
    "epsilon = 0.1\n",
    "sigma = dati_illeciti['tentativi'].std()\n",
    "\n",
    "n_0 = (Z.ppf(1.99/2) * sigma / epsilon)**2\n",
    "print(n_0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__4.__ Ipotizziamo che $Y \\sim \\mathrm G(h)$, e che $h$ sia sconosciuto. Proponete uno stimatore per $h$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__5.__ Indicate se lo stimatore proposto al punto precedente gode di particolari proprietà, giustificando la vostra risposta."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__6.__ Applicate lo stimatore proposto al punto 4 per ottenere una stima $\\hat h$ del parametro sconosciuto $h$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.2852600377256804\n"
     ]
    }
   ],
   "source": [
    "h_hat = 1 / (1 + dati_illeciti['tentativi'].mean())\n",
    "print(h_hat)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nel resto dell'esercizio, calcolate le probabilità richieste facendo riferimento al modello assunto per $Y$ e sostituendo a $h$ la stima $\\hat h$ ottenuta al punto precedente."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__7.__ Calcolate la probabilità $\\mathbb P(3 < X < 8)$ che il numero di tentativi di autenticazione durante un accesso illecito sia strettamente compreso tra 3 e 8."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.26983959225517173\n"
     ]
    }
   ],
   "source": [
    "Y = st.geom(h_hat)\n",
    "\n",
    "print(Y.cdf(7) - Y.cdf(3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__8.__ Un malintenzionato ha effettuato due tentativi di accesso andati a vuoto. Calcolate la probabilità che siano necessari più di due ulteriori tentativi di accesso."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(0.7147399622743196)"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1 - Y.cdf(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "P(Y >= 2 + 2 | Y >= 2) = P(Y >= 2) = 1 - P(Y <= 1)"
   ]
  }
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