2017年5月1日月曜日

学習環境

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)、重複試行の確率、問32、33、34、35、36.を取り組んでみる。


  1. p=0.5 0.0625( 1+2+2.5+20·0.125 ) =0.0625·8 =0.5 p=0.3 0.0081( 1+2.8+4.9+20*0.343 ) =0.126036 0.126

    1. ( 10 4 ) 1 2 10 = 10·9·8·7 4·3·2 · 1 2 10 =10·3·7· 1 2 10 = 105 512

    2. ( 10 5 ) 1 2 10 = 10·9·8·7·6 5·4·3·2 · 1 2 10 = 9·7 2 9 = 63 512

    3. ( 10 0 ) 1 2 10 +( 10 1 ) 1 2 10 +( 10 2 ) 1 2 10 +( 10 3 ) 1 2 10 = 1 2 10 ( 1+10+45+120 ) = 176 1024 = 11 64

    1. ( 5 2 ) ( 2 6 ) 2 · ( 4 6 ) 3 = 10·8 3 5 = 80 243

    2. 1( ( 5 0 ) ( 2 6 ) 0 · ( 4 6 ) 5 +( 5 1 ) ( 2 6 ) 1 · ( 4 6 ) 4 ) =1 32+5·16 3 5 =1 32+80 3 5 =1 112 243 = 131 243

    1. ( 8 4 ) ( 1 2 ) 8 = 8·7·6·5 4·3·2 · 1 2 8 = 35 128

    2. ( 8 3 ) ( 1 2 ) 8 = 8·7·6 3·2 · 1 2 8 = 7 32

    3. ( 8 2 ) ( 1 2 ) 8 = 8·7 2 · 1 2 8 = 7 64

  2. ( n 0 ) 1 2 n +( n 2 ) 1 2 n +··· = 2 n1 2 n = 1 2 1 1 2 = 1 2

コード(Emacs)

HTML5

<div id="graph0"></div>
<pre id="output0"></pre>
n = <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="sample32.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 output = () => {
    p('36-4. 表');
    let n = parseInt(input_n.value, 10),
        points = [];

    points = range(n).map((i) => {
        return [i + 1,
                range(i + 1)
                .map(() => Math.floor(Math.random() * 2))
                .filter((b) => b === 0)
                .length / (i + 1)]
    });
    
    let t = points[points.length - 1][1],
        result = 1 / 2;
    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();

n = 

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