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)
- Nebo(Windows アプリ)
- iPad Pro + Apple Pencil
- MyScript Nebo(iPad アプリ)
- 参考書籍
数学読本〈6〉線形写像・1次変換/数論へのプレリュード/集合論へのプレリュード/εとδ/落ち穂拾い など(松坂 和夫(著)、岩波書店)の第26章(エピローグ - 落ち穂拾い、など)、26.4(確率分布と平均)、確率変数の平均または期待値、問8.を取り組んでみる。
コード(Emacs)
Python 3
#!/usr/bin/env python3 from sympy import pprint, symbols, combinatorial, Rational import random print('8.') n = 1000000 dice = range(1, 7) a = 1 p = 1 / 6 print(f'期待値{2 / p}') t = 0 for i in range(n): s = 0 while True: s += 1 b = random.choice(dice) if b == a: while True: s += 1 b = random.choice(dice) if b == a: break break if i % 100000 == 0: print(s) t += s print(f'試行回数 {n}回: {t / n}')
入出力結果(Terminal, Jupyter(IPython))
$ ./sample10.py 8. 期待値12.0 3 18 5 12 8 24 6 12 21 2 試行回数 1000000回: 11.994299 $
HTML5
<div id="graph0"></div> <pre id="output0"></pre> <label for="r0">r = </label> <input id="r0" type="number" min="0" value="1"> <label for="dx">dx = </label> <input id="dx" type="number" min="0" step="0.001" value="1"> <br> <label for="x1">x1 = </label> <input id="x1" type="number" value="1"> <label for="x2">x2 = </label> <input id="x2" type="number" value="1000"> <br> <label for="y1">y1 = </label> <input id="y1" type="number" value="0"> <label for="y2">y2 = </label> <input id="y2" type="number" value="20"> <button id="draw0">draw</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="sample10.js"></script>
JavaScript
let div0 = document.querySelector('#graph0'), pre0 = document.querySelector('#output0'), width = 600, height = 600, padding = 50, btn0 = document.querySelector('#draw0'), btn1 = document.querySelector('#clear0'), input_r = document.querySelector('#r0'), input_dx = document.querySelector('#dx'), input_x1 = document.querySelector('#x1'), input_x2 = document.querySelector('#x2'), input_y1 = document.querySelector('#y1'), input_y2 = document.querySelector('#y2'), inputs = [input_r, input_dx, input_x1, input_x2, input_y1, input_y2], p = (x) => pre0.textContent += x + '\n'; let f = (x) => { let t = 0; for (let i = 0; i < x; i += 1) { let s = 0; for (;;) { s += 1; if (Math.floor(Math.random() * 6) == 0) { for (;;) { s += 1; if (Math.floor(Math.random() * 6) == 0) { break; } } break; } } t += s; } return t / x; }; let draw = () => { pre0.textContent = ''; let r = parseFloat(input_r.value), dx = parseFloat(input_dx.value), x1 = parseFloat(input_x1.value), x2 = parseFloat(input_x2.value), y1 = parseFloat(input_y1.value), y2 = parseFloat(input_y2.value); if (r === 0 || dx === 0 || x1 > x2 || y1 > y2) { return; } let points = [], lines = [[x1, 12, x2, 12, 'red']], fns = [[f, 'green']]; fns .forEach((o) => { let [f, color] = o; for (let x = x1; x <= x2; x += dx) { let y = f(x); points.push([x, y, color]); } }); let xscale = d3.scaleLinear() .domain([x1, x2]) .range([padding, width - padding]); let yscale = d3.scaleLinear() .domain([y1, y2]) .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('line') .data([[x1, 0, x2, 0], [0, y1, 0, y2]].concat(lines)) .enter() .append('line') .attr('x1', (d) => xscale(d[0])) .attr('y1', (d) => yscale(d[1])) .attr('x2', (d) => xscale(d[2])) .attr('y2', (d) => yscale(d[3])) .attr('stroke', (d) => d[4] || 'black'); svg.selectAll('circle') .data(points) .enter() .append('circle') .attr('cx', (d) => xscale(d[0])) .attr('cy', (d) => yscale(d[1])) .attr('r', r) .attr('fill', (d) => d[2] || 'green'); svg.append('g') .attr('transform', `translate(0, ${height - padding})`) .call(xaxis); svg.append('g') .attr('transform', `translate(${padding}, 0)`) .call(yaxis); [fns].forEach((fs) => p(fs.join('\n'))); }; inputs.forEach((input) => input.onchange = draw); btn0.onclick = draw; btn1.onclick = () => pre0.textContent = ''; draw();
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