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Update i guess

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Steffo 2020-01-16 18:51:38 +01:00
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31 changed files with 1149 additions and 113 deletions
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uni.steffo.eu

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docs/sw.js
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@ -1 +1 @@
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src/components/hypothesis.css Normal file
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@ -0,0 +1,3 @@
.hypothesis {
}

15
src/components/hypothesis.js Normal file
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@ -0,0 +1,15 @@
import style from "./hypothesis.css";
import {Component} from "preact";
export default class Hypothesis extends Component {
render() {
return (
<div class={style.hypothesis}>
<h4>
Ipotesi
</h4>
{this.props.children}
</div>
)
}
}

6
src/components/panel.js
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@ -2,6 +2,10 @@ import style from "./panel.css";
import { Component } from 'preact';
export default class Panel extends Component {
getStyle() {
return style.panel;
};
render() {
let title = null;
if(this.props.title !== undefined) {
@ -9,7 +13,7 @@ export default class Panel extends Component {
}
return (
<div class={style.panel} id={this.props.id}>
<div class={this.getStyle()} id={this.props.id}>
{title}
{this.props.children}
</div>

0
docs/.nojekyll → src/components/proof.css
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15
src/components/proof.js Normal file
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@ -0,0 +1,15 @@
import style from "./proof.css";
import {Component} from "preact";
export default class Proof extends Component {
render() {
return (
<div class={style.proof}>
<h4>
Dimostrazione
</h4>
{this.props.children}
</div>
)
}
}

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src/components/theorem.css Normal file
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@ -0,0 +1,4 @@
.theorem {
background-color: rgba(160, 255, 204, 0.1);
color: #a0ffcc;
}

8
src/components/theorem.js Normal file
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@ -0,0 +1,8 @@
import style from "./theorem.css";
import Panel from "./panel.js";
export default class Theorem extends Panel {
getStyle() {
return super.getStyle() + " " + style.theorem;
}
}

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src/components/thesis.css Normal file
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@ -0,0 +1,3 @@
.thesis {
}

15
src/components/thesis.js Normal file
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@ -0,0 +1,15 @@
import style from "./thesis.css";
import {Component} from "preact";
export default class Thesis extends Component {
render() {
return (
<div class={style.thesis}>
<h4>
Tesi
</h4>
{this.props.children}
</div>
)
}
}

10
src/index.css
View file

@ -9,13 +9,21 @@ body {
}
h1, h2, h3, h4, h5, h6 {
text-align: center;
margin-top: 4px;
margin-bottom: 4px;
color: #ffffff;
font-weight: normal;
}
h1, h2, h3 {
text-align: center;
}
h4, h5, h6 {
font-weight: bold;
}
a {
color: #00caca;
text-decoration: none;

3
src/pages/home.js
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@ -14,6 +14,9 @@ export default class Home extends Component {
<p>
Appunti scritti mentre studiavo per l'esame di <a href={"http://personale.unimore.it/rubrica/contenutiad/llarocca/2019/58028/N0/N0/9999"}>Statistica ed elementi di probabilità</a> del <a href="https://www.unimore.it/didattica/mlaurea.html?ID=54">corso triennale di Informatica</a> all'<a href="https://www.unimore.it/">Unimore</a> del Prof. <a href={"http://personale.unimore.it/rubrica/dettaglio/llarocca"}>Luca La Rocca</a>.
</p>
<p>
<Todo>TODO: è ancora incompleto!</Todo>
</p>
</Panel>
<Panel title={<a href="https://github.com/Steffo99/cleaver">Cleaver</a>}>
<p>

163
src/pages/statistica.js
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@ -6,6 +6,10 @@ import Split from '../components/split';
import Plus from '../components/plus';
import Minus from '../components/minus';
import Todo from '../components/todo';
import Theorem from "../components/theorem";
import Hypothesis from "../components/hypothesis";
import Thesis from "../components/thesis";
import Proof from "../components/proof";
const r = String.raw;
@ -304,42 +308,187 @@ export default class Statistica extends Component {
<Split>
<Panel title={"Disposizioni"}>
<p>
Estraggo un numero, mi segno che numero ho estratto e lo <b>tengo fuori dal sacchetto</b>.
Estraggo un numero, da un sacchetto con <Latex>n</Latex> numeri, mi segno che numero ho estratto e lo <b>tengo fuori dal sacchetto</b>. Ripeto per <Latex>k</Latex> volte.
</p>
<p>
<b>Tengo conto</b> dell'ordine in cui ho estratto i numeri.
</p>
<p>
<Latex>{r`\boldsymbol{D}_{n, k} = \frac{n!}{(n - k)!}`}</Latex>
</p>
</Panel>
<Panel title={"Disposizioni con ripetizione"}>
<p>
Estraggo un numero, mi segno che numero ho estratto e lo <b>rimetto nel sacchetto</b>.
Estraggo un numero, da un sacchetto con <Latex>n</Latex> numeri, mi segno che numero ho estratto e lo <b>rimetto nel sacchetto</b>. Ripeto per <Latex>k</Latex> volte.
</p>
<p>
<b>Tengo conto</b> dell'ordine in cui ho estratto i numeri.
</p>
<p>
<Latex>{r`\boldsymbol{D}^{r}_{n, k} = n^k`}</Latex>
</p>
</Panel>
<Panel title={"Combinazioni"}>
<p>
Estraggo un numero, mi segno che numero ho estratto e lo <b>tengo fuori dal sacchetto</b>.
Estraggo un numero, da un sacchetto con <Latex>n</Latex> numeri, mi segno che numero ho estratto e lo <b>tengo fuori dal sacchetto</b>. Ripeto per <Latex>k</Latex> volte.
</p>
<p>
<b>Non mi interessa</b> l'ordine in cui ho estratto i numeri.
</p>
<p>
<Latex>{r`\boldsymbol{C}_{n, k} = \binom{n}{k} = \frac{n!}{(k)! \cdot (n - k)!}`}</Latex>
</p>
</Panel>
<Panel title={"Combinazioni con ripetizione"}>
<p>
Estraggo un numero, mi segno che numero ho estratto e lo <b>rimetto nel sacchetto</b>.
Estraggo un numero, da un sacchetto con <Latex>n</Latex> numeri, mi segno che numero ho estratto e lo <b>rimetto nel sacchetto</b>. Ripeto per <Latex>k</Latex> volte.
</p>
<p>
<b>Non mi interessa</b> l'ordine in cui ho estratto i numeri.
</p>
</Panel>
<Panel title={"Permutazioni"}>
<p>
Estraggo N numeri e guardo in quanti ordini diversi li posso mettere.
<Latex>{r`\boldsymbol{C}^{r}_{n, k} = \binom{n + k - 1}{k} = \frac{(n + k - 1)!}{(k)! \cdot (n - 1)!}`}</Latex>
</p>
<p>
<Todo>TODO: Controllare la formula.</Todo>
</p>
</Panel>
</Split>
<Split>
<Panel title={"Permutazioni"}>
<p>
Estraggo <Latex>n</Latex> numeri e guardo in quanti ordini diversi li posso mettere.
</p>
<p>
<Latex>{r`\boldsymbol{P}_n = n!`}</Latex>
</p>
</Panel>
</Split>
<Split>
<Panel title={"Spazi equiprobabili geometrici"}>
<p>
Gli spazi campionari possono avere un numero infinito di esisti: si ha equiprobabilità se nessun esito è privilegiato rispetto agli altri.
</p>
</Panel>
</Split>
<Split title={"Probabilità condizionata"}>
<Panel title={<span>E dato F</span>}>
<p>
La probabilità di un evento <Latex>E</Latex> dato un altro evento <Latex>F</Latex> indica la probabilità che si verifichi <Latex>E</Latex> sapendo che <b>si è già verificato</b> <Latex>F</Latex>.
</p>
<p>
<Latex>{r`P(E|F) = \frac{P(E \cap F)}{P(F)}`}</Latex>
</p>
</Panel>
<Panel title={"Eventi indipendenti"}>
<p>
Se due eventi sono indipendenti, sapere che uno dei due si è verificato non influisce sulle probabilità che si sia verificato l'altro.
</p>
<p>
<Latex>{r`E, F\ indipendenti\ \Longleftrightarrow P(E|F) = P(E), P(F|E) = P(F)`}</Latex>
</p>
</Panel>
<Panel title={"Eventi mutualmente esclusivi"}>
<p>
Se due eventi sono mutualmente esclusivi, entrambe le loro probabilità condizionate saranno uguali a 0.
</p>
<p>
<Latex>{r`E \cap F = \emptyset \Longleftrightarrow P(E|F) = P(F|E) = 0`}</Latex>
</p>
</Panel>
<Panel title={"Regola della catena"}>
<p>
Si può sfruttare la formula inversa della probabilità condizionata per calcolare catene di intersezioni:
</p>
<p>
<Latex>{r`P(E_1 \cap \times \cap E_n) = P(E_1) \times P(E_2 | E_1) \times \dots \times P(E_n | E_1 \cap E_2 \cap \dots \cap E_{n-1})`}</Latex>
</p>
</Panel>
</Split>
<Split>
<Panel title={"Partizioni"}>
<p>
E' una partizione dello spazio campionario un insieme di eventi:
</p>
<ul>
<li><b>Finito</b>.</li>
<li>In cui tutti gli eventi hanno <b>probabilità diversa da 0</b>.</li>
<li>In cui tutti gli eventi sono <b>mutualmente esclusivi</b>.</li>
<li>L'unione di tutti gli eventi <b>copre lo spazio campionario</b>.</li>
</ul>
<p>
Se lo spazio campionario fosse una torta, una sua partizione sarebbe l'insieme delle fette di uno dei modi in cui si potrebbe tagliare.
</p>
<p>
La partizione <Latex>{r`E_i`}</Latex> è composta dagli eventi <Latex>{r`E_1`}</Latex>, <Latex>{r`E_2`}</Latex>, <Latex>{r`E_3`}</Latex>, fino a <Latex>{r`E_n`}</Latex>.
</p>
</Panel>
<Theorem title={"Legge delle alternative"}>
<Hypothesis>
<ul>
<li><Latex>E_i</Latex> <b>partizione</b> di <Latex>{r`\Omega`}</Latex></li>
<li><Latex>{r`F`}</Latex> <b>evento</b> <Latex>{r`\in \Omega`}</Latex></li>
</ul>
</Hypothesis>
<Thesis>
<p>
La probabilità che si verifichi un evento è pari alla somma delle probabilità dell'evento stesso dati tutti gli eventi di una partizione.
</p>
<p>
<Latex>{r`P(F) = \sum_{i} P(F|E_i) \cdot P(E_i)`}</Latex>
</p>
</Thesis>
<Proof>
<p>
Per la definizione di probabilità condizionata:
</p>
<p>
<Latex>{r`P(F|E_i) \cdot P(E_i) = P(F \cap E_i)`}</Latex>
</p>
<p>
Essendo parte di una partizione, tutti gli <Latex>E_i</Latex> sono distinti:
</p>
<p>
<Latex>{r`\forall i, \exists! E_i`}</Latex>
</p>
<p>
Essendo mutualmente esclusivi, le probabilità di tutti gli <Latex>E_i</Latex> possono essere sommate:
</p>
<p>
<Latex>{r`\sum_i P(F \cap E_i) = P \left( \bigcup_i (F \cap E_i) \right)`}</Latex>
</p>
<p>
Essendo una partizione di <Latex>{r`\Omega`}</Latex>, allora la loro unione lo forma:
</p>
<p>
<Latex>{r`\bigcup_i ( F \cap E_i ) = F \cap \left( \bigcup_i E_i \right) = F \cap \Omega = F`}</Latex>
</p>
</Proof>
</Theorem>
</Split>
<Split>
<Panel title={"Legge condizionata delle alternative"}>
<p>
La legge delle alternative funziona anche per gli eventi, non solo per <Latex>{r`\Omega`}</Latex>:
</p>
<p>
<Latex>{r`P(F|G) = \sum_i P(F|E_i \cap G) \cdot P(E_i | G)`}</Latex>
</p>
</Panel>
</Split>
<Split>
<Theorem title={"Formula di Bayes"}>
<Hypothesis>
</Hypothesis>
<Thesis>
</Thesis>
<Proof>
</Proof>
</Theorem>
</Split>
</div>
)
}