数学 - JavaScript - 確からしさをみる - 確率 – 条件つき確率と確率の乗法定理 - 独立事象と従属事象

学習環境

Surface 3 (4G LTE)、Surface 3 タイプカバー、Surface ペン(端末)
Windows 10 Pro (OS)
数式入力ソフト(TeX, MathML): MathType
MathML対応ブラウザ: Firefox、Safari
MathML非対応ブラウザ(Internet Explorer, Google Chrome...)用JavaScript Library: MathJax

数学読本〈4〉数列の極限，順列/順列・組合せ/確率/関数の極限と微分法(松坂和夫(著)、岩波書店)の第16章(確からしさをみる - 確率)、16.2(条件つき確率と確率の乗法定理)、独立事象と従属事象、問29、30、31.を取り組んでみる。

$\begin{array}{l} P_{A} (B) = \frac{2}{3} \\ P_{A} (B) \neq P (B) \\ P_{A} (C) = \frac{1}{3} \\ P_{A} (C) = P (C) \end{array}$
1. $\begin{array}{l} P (A) = \frac{13}{52} = \frac{1}{4} \\ P (B) = \frac{3 \cdot 4}{52} = \frac{3}{13} \\ P (A) \cdot P (B) = \frac{3}{52} \\ P (A \cap B) = \frac{3}{52} = \frac{3}{52} \\ 独立事象 \end{array}$
2. $\begin{array}{l} P (A) = \frac{3}{6} = \frac{1}{2} \\ P (B) = \frac{2}{6} = \frac{1}{3} \\ P (A) \cdot P (B) = \frac{1}{6} \\ P (A \cap B) = \frac{1}{6} \\ 独立事象 \end{array}$
3. $\begin{array}{l} P (A) = \frac{1}{2} \\ P (B) = \frac{1}{2} \\ P (A) \cdot P (B) = \frac{1}{4} \\ P (A \cap B) = \frac{1}{4} \\ 独立事象 \end{array}$
4. $\begin{array}{l} P (A) = \frac{13 \cdot 39}{52 \cdot 51} = \frac{13}{4 \cdot 17} = \frac{13}{68} \\ P (B) = \frac{13 \cdot 12}{52 \cdot 51} + \frac{39 \cdot 13}{52 \cdot 51} = \frac{4 + 13}{4 \cdot 17} = \frac{1}{4} \\ P (A \cap B) = \frac{13 \cdot 13}{52 \cdot 51} = \frac{13}{4 \cdot 51} = \frac{13}{204} \\ P (A) P (B) = \frac{13}{272} \\ P (A \cap B) \neq P (A) P (B) \end{array}$
$\begin{array}{l} P (A) = p \\ P (A^{'}) = 1 - p \\ P (B) = q \\ P (A \cap B) = p q \\ P (A^{'}) P (B) = (1 - p) q \\ P (A^{'} \cap B) \\ = P (B) - P (A \cap B) \\ = q - p q \\ = (1 - p) q \\ P (A^{'} \cap B) = P (A^{'}) P (B) \end{array}$

コード(Emacs)

HTML5

<div id="graph0"></div>
<pre id="output0"></pre>
ÂõûÊï∞: <input id="n0" type="number" min="1" step="1" value="1000">
<br>
<button id="run0">run</button>
<button id="clear0">clear</button>

<script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/d3/4.2.6/d3.min.js" integrity="sha256-5idA201uSwHAROtCops7codXJ0vja+6wbBrZdQ6ETQc=" crossorigin="anonymous"></script>
<script src="sample29.js"></script>

JavaScript

let pre0 = document.querySelector('#output0'),
    input_n = document.querySelector('#n0'),
    btn0 = document.querySelector('#run0'),
    btn1 = document.querySelector('#clear0'),
    div0 = document.querySelector('#graph0'),
    width = 600,
    height = 600,
    padding = 50,
    p = (x) => pre0.textContent += x + '\n';

let range = (n) => {
    let result = [];
    for (let i = 0; i < n; i += 1) {
        result.push(i);
    }
    return result;
};

let suit = range(13).map(() => 0)
    .concat(range(13).map(() => 1))
    .concat(range(13).map(() => 2))
    .concat(range(13).map(() => 3)),
    spade = 0,
    club = 1,
    dia = 2,
    heart = 3;

let f = () => {
    let suit0 = suit.slice(),
        i = Math.floor(Math.random() * suit0.length),
        card1 = suit[i];

    suit0.splice(i, 1);
    i = Math.floor(Math.random() * suit0.length);
    let card2 = suit[i];

    return card1 === heart && card2 === spade;
};
let output = () => {
    p('30-4.');
    let n = parseInt(input_n.value, 10),
        results = range(n).map(() => f()),
        points = [];

    points = range(n).map((i) => {
        return [i + 1,
                range(i + 1)
                .map(() => f())
                .filter((b) => b)
                .length / (i + 1)]
    });
    
    let t = points[points.length - 1][1],
        result = 13 / 204;
    p(t ===  result);
    p(t);
    p(result);
    p(Math.abs(t - result));

    let xscale = d3.scaleLinear()
        .domain([1, n])
        .range([padding, width - padding]);
    let yscale = d3.scaleLinear()
        .domain([0, 1])
        .range([height - padding, padding]);

    let xaxis = d3.axisBottom().scale(xscale);
    let yaxis = d3.axisLeft().scale(yscale);
    div0.innerHTML = '';
    let svg = d3.select('#graph0')
        .append('svg')
        .attr('width', width)
        .attr('height', height);

    svg.selectAll('circle')
        .data(points)
        .enter()
        .append('circle')
        .attr('cx', (d) => xscale(d[0]))
        .attr('cy', (d) => yscale(d[1]))
        .attr('r', 1)
        .attr('fill', 'green');

    svg.append('g')
        .attr('transform', `translate(0, ${height - padding})`)
        .call(xaxis);

    svg.append('g')
        .attr('transform', `translate(${padding}, 0)`)
        .call(yaxis);
};

input_n.onchange = output;
btn0.onclick = output;
btn1.onclick = () => pre0.textContent = '';

output();

回数:

Kamimura's blog

2017年4月30日日曜日

数学 - JavaScript - 確からしさをみる - 確率 – 条件つき確率と確率の乗法定理 - 独立事象と従属事象

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