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Update i guess
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{"version":3,"sources":["webpack:///./D:/Codice/appuntiweb/src/index.css","webpack:///./components/D:/Codice/appuntiweb/src/components/panel.css","webpack:///./components/D:/Codice/appuntiweb/src/components/split.css","webpack:///./components/D:/Codice/appuntiweb/src/components/todo.css","webpack:///./components/D:/Codice/appuntiweb/src/components/latex.css","webpack:///./components/D:/Codice/appuntiweb/src/components/plus.css","webpack:///./components/D:/Codice/appuntiweb/src/components/minus.css","webpack:///./components/D:/Codice/appuntiweb/src/components/copyright.css"],"names":[],"mappings":"AAAA,EACC,8BAAuB,sBAGxB,KACC,yBACA,cACA,sBAAwB,CAGzB,kBACC,kBACA,eACA,kBACA,WACA,eAAoB,CAGrB,EACI,cACA,oBAAsB,CAG1B,QACC,aAAe,CAGhB,SACC,UAAe,CAGhB,IACC,cAAgB,CChCjB,cACI,sCACA,YACA,kBACA,WACA,wBACA,eAAiB,CCFrB,oBACI,oBAAc,iCACd,mBAAgB,eAGpB,mBACI,mBAAa,gCACb,oBAAe,cACf,0BAAc,aCZlB,aACI,sBACA,kBACA,YACA,sBACA,UAAc,CCLlB,cACI,qBACA,qBAAuB,CCF3B,aACI,aAAe,CCDnB,cACI,aAAe,CCDnB,kBACI,eACA,WACA,kBACA,iBAAmB","file":"style.bc35d.css","sourcesContent":["* {\n\tbox-sizing: border-box;\n}\n\nbody {\n\tbackground-color: #0d193b;\n\tcolor: #a0ccff;\n\tfont-family: sans-serif;\n}\n\nh1, h2, h3, h4, h5, h6 {\n\ttext-align: center;\n\tmargin-top: 4px;\n\tmargin-bottom: 4px;\n\tcolor: #ffffff;\n\tfont-weight: normal;\n}\n\na {\n color: #00caca;\n text-decoration: none;\n}\n\na:hover {\n\tcolor: #4affff;\n}\n\na:active {\n\tcolor: #ffffff;\n}\n\nimg {\n\tmax-width: 100%;\n}\n\n\n// WEBPACK FOOTER //\n// ./D:/Codice/appuntiweb/src/index.css",".panel {\n background-color: rgba(62.7%, 80%, 100%, 0.1);\n padding: 4px;\n border-radius: 4px;\n margin: 4px;\n height: calc(100% - 8px);\n min-width: 256px;\n}\n\n\n\n// WEBPACK FOOTER //\n// ./components/D:/Codice/appuntiweb/src/components/panel.css",".split {\n\n}\n\n.splitparent {\n display: flex;\n flex-wrap: wrap;\n}\n\n.splitchild {\n flex-grow: 1;\n flex-shrink: 0;\n flex-basis: 0;\n}\n\n\n\n// WEBPACK FOOTER //\n// ./components/D:/Codice/appuntiweb/src/components/split.css",".todo {\r\n border: 4px yellow solid;\r\n border-radius: 4px;\r\n padding: 2px;\r\n background-color: black;\r\n color: yellow;\r\n}\r\n\n\n\n// WEBPACK FOOTER //\n// ./components/D:/Codice/appuntiweb/src/components/todo.css",".latex {\n display: inline-block;\n vertical-align: middle;\n}\n\n\n\n// WEBPACK FOOTER //\n// ./components/D:/Codice/appuntiweb/src/components/latex.css",".plus {\r\n color: #ff7d7d;\r\n}\r\n\n\n\n// WEBPACK FOOTER //\n// ./components/D:/Codice/appuntiweb/src/components/plus.css",".minus {\r\n color: #7d7dff;\r\n}\r\n\n\n\n// WEBPACK FOOTER //\n// ./components/D:/Codice/appuntiweb/src/components/minus.css",".copyright {\r\n margin-top: 8px;\r\n color: white;\r\n text-align: center;\r\n font-size: x-small;\r\n}\n\n\n// WEBPACK FOOTER //\n// ./components/D:/Codice/appuntiweb/src/components/copyright.css"],"sourceRoot":""}
|
|
@ -1 +1 @@
|
|||
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"use strict";var precacheConfig=[["/assets/favicon.ico","468bad0a3f47a965985c8a99f3ab0ced"],["/assets/icon.png","2b714cf154cd80b3949545dfe0c5939a"],["/bundle.4130c.js","5e2456bbf2ba8e1299fa9a8f024e9aac"],["/favicon.ico","468bad0a3f47a965985c8a99f3ab0ced"],["/index.html","87816bddf0d30dedcb21d904c6bb3bbe"],["/manifest.json","451674ae8f01fd50402a3afd4ebeeffa"],["/style.114f1.css","c7ce12d23f38743501695346c60db250"]],cacheName="sw-precache-v3-sw-precache-webpack-plugin-"+(self.registration?self.registration.scope:""),ignoreUrlParametersMatching=[/^utm_/],addDirectoryIndex=function(e,t){var n=new URL(e);return"/"===n.pathname.slice(-1)&&(n.pathname+=t),n.toString()},cleanResponse=function(e){return e.redirected?("body"in e?Promise.resolve(e.body):e.blob()).then(function(t){return new Response(t,{headers:e.headers,status:e.status,statusText:e.statusText})}):Promise.resolve(e)},createCacheKey=function(e,t,n,r){var a=new URL(e);return r&&a.pathname.match(r)||(a.search+=(a.search?"&":"")+encodeURIComponent(t)+"="+encodeURIComponent(n)),a.toString()},isPathWhitelisted=function(e,t){if(0===e.length)return!0;var n=new URL(t).pathname;return e.some(function(e){return n.match(e)})},stripIgnoredUrlParameters=function(e,t){var n=new URL(e);return n.hash="",n.search=n.search.slice(1).split("&").map(function(e){return e.split("=")}).filter(function(e){return t.every(function(t){return!t.test(e[0])})}).map(function(e){return e.join("=")}).join("&"),n.toString()},hashParamName="_sw-precache",urlsToCacheKeys=new Map(precacheConfig.map(function(e){var t=e[0],n=e[1],r=new URL(t,self.location),a=createCacheKey(r,hashParamName,n,!1);return[r.toString(),a]}));function setOfCachedUrls(e){return e.keys().then(function(e){return e.map(function(e){return e.url})}).then(function(e){return new Set(e)})}self.addEventListener("install",function(e){e.waitUntil(caches.open(cacheName).then(function(e){return setOfCachedUrls(e).then(function(t){return Promise.all(Array.from(urlsToCacheKeys.values()).map(function(n){if(!t.has(n)){var r=new Request(n,{credentials:"same-origin"});return fetch(r).then(function(t){if(!t.ok)throw new Error("Request for "+n+" returned a response with status "+t.status);return cleanResponse(t).then(function(t){return e.put(n,t)})})}}))})}).then(function(){return self.skipWaiting()}))}),self.addEventListener("activate",function(e){var t=new Set(urlsToCacheKeys.values());e.waitUntil(caches.open(cacheName).then(function(e){return e.keys().then(function(n){return Promise.all(n.map(function(n){if(!t.has(n.url))return e.delete(n)}))})}).then(function(){return self.clients.claim()}))}),self.addEventListener("fetch",function(e){if("GET"===e.request.method){var t,n=stripIgnoredUrlParameters(e.request.url,ignoreUrlParametersMatching);(t=urlsToCacheKeys.has(n))||(n=addDirectoryIndex(n,"index.html"),t=urlsToCacheKeys.has(n));!t&&"navigate"===e.request.mode&&isPathWhitelisted(["^(?!\\/__).*"],e.request.url)&&(n=new URL("index.html",self.location).toString(),t=urlsToCacheKeys.has(n)),t&&e.respondWith(caches.open(cacheName).then(function(e){return e.match(urlsToCacheKeys.get(n)).then(function(e){if(e)return e;throw Error("The cached response that was expected is missing.")})}).catch(function(t){return console.warn('Couldn\'t serve response for "%s" from cache: %O',e.request.url,t),fetch(e.request)}))}});
|
3
src/components/hypothesis.css
Normal file
3
src/components/hypothesis.css
Normal file
|
@ -0,0 +1,3 @@
|
|||
.hypothesis {
|
||||
|
||||
}
|
15
src/components/hypothesis.js
Normal file
15
src/components/hypothesis.js
Normal file
|
@ -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>
|
||||
)
|
||||
}
|
||||
}
|
|
@ -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>
|
||||
|
|
15
src/components/proof.js
Normal file
15
src/components/proof.js
Normal file
|
@ -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>
|
||||
)
|
||||
}
|
||||
}
|
4
src/components/theorem.css
Normal file
4
src/components/theorem.css
Normal file
|
@ -0,0 +1,4 @@
|
|||
.theorem {
|
||||
background-color: rgba(160, 255, 204, 0.1);
|
||||
color: #a0ffcc;
|
||||
}
|
8
src/components/theorem.js
Normal file
8
src/components/theorem.js
Normal file
|
@ -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;
|
||||
}
|
||||
}
|
3
src/components/thesis.css
Normal file
3
src/components/thesis.css
Normal file
|
@ -0,0 +1,3 @@
|
|||
.thesis {
|
||||
|
||||
}
|
15
src/components/thesis.js
Normal file
15
src/components/thesis.js
Normal file
|
@ -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>
|
||||
)
|
||||
}
|
||||
}
|
|
@ -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;
|
||||
|
|
|
@ -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>
|
||||
|
|
|
@ -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>
|
||||
)
|
||||
}
|
||||
|
|
Loading…
Reference in a new issue