31:[] 2f:{"title":"Uniform distribution","cells":[{"id":38,"value":"# Uniform distribution","pinned":false,"hidden":false,"mode":"md"},{"id":627,"value":"

${tex`X\\sim \\operatorname{Uniform}(a,b)`}, for ${tex`X \\in [a,b]`}","pinned":false,"hidden":false,"mode":"md"},{"id":496,"value":"## Density function and moments","pinned":false,"hidden":false,"mode":"md"},{"id":618,"value":"tex`X\\sim \\mathrm{Uniform}(a,b)`","pinned":false,"hidden":false,"mode":"ojs"},{"id":118,"value":"viewof params = Inputs.form([\n Inputs.range([-5, 5], {value: 0, step: 0.1, label: tex`a:`}),\n Inputs.range([-5, 5], {value: 1, step: 0.1, label: tex`b:`}),\n Inputs.range([-5, 5], {value: 1, step: 0.01, label: \"quantile:\"})\n ])","pinned":false,"hidden":false,"mode":"ojs"},{"id":461,"value":"dist_quantile = tex`\\text{If } X \\sim \\operatorname{Uniform}(${params[0]},${params[1]}) \\text{ then } `","pinned":false,"hidden":false,"mode":"ojs"},{"id":555,"value":"moments = tex`\n\\begin{aligned}\n&E( X) =\\frac{a+b}{2} = ${((params[0] + params[1])/2).toPrecision(3)} \\\\[1em]\n&Var( X) =\\frac{(b-a)^2}{12} = ${(((params[1]-params[0])**2)/12).toPrecision(3)} \\\\[1em]\n&P( X\\leq ${params[2]}) =${unifcdf.toPrecision(4)}\n\\end{aligned}\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":305,"value":"plt_pdf = Plot.plot({\n color: {\n legend: true\n },\n x: {\n label: \"x\",\n axis: true,\n domain: [-5.5,5.5]\n },\n y: {\n label: \"f(x)\",\n axis: true,\n domain: [0,1.1/(params[1]-params[0])]\n },\n marks: [\n Plot.ruleY([0]),\n //Plot.ruleX([0]),\n Plot.line(unifpdf, {x: \"x\", y: \"pdf\", stroke : \"green\", strokeWidth: 2}),\n Plot.areaY(unifpdf, {filter: d => d.x <= params[2], x: \"x\", y: \"pdf\", fill: \"green\", opacity: 0.2})\n ]\n })","pinned":false,"hidden":false,"mode":"ojs"},{"id":109,"value":"
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\n\n---\n## 🙈 Appendix 🙈\n\nHere is just some code and data defintions that you probably don't want to read.","pinned":false,"hidden":false,"mode":"md"},{"id":221,"value":"#### Imports","pinned":false,"hidden":false,"mode":"md"},{"id":26,"value":"jstat = require('jstat')","pinned":false,"hidden":false,"mode":"ojs"},{"id":223,"value":"#### Data","pinned":false,"hidden":false,"mode":"md"},{"id":17,"value":"unifpdf = {\n const x = d3.range(-5.1, 5.1, 0.001);\n const unifpdf = x.map(x => ({x: x, pdf: jstat.uniform.pdf(x, params[0], params[1])}));\n return unifpdf\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":19,"value":"unifcdf = jstat.uniform.cdf(params[2], params[0], params[1]);","pinned":false,"hidden":false,"mode":"ojs"},{"id":229,"value":"#### Style","pinned":false,"hidden":false,"mode":"md"},{"id":202,"value":"","pinned":false,"hidden":false,"mode":"html"},{"id":58,"value":"viewof md_colour = Inputs.color({label: \"Highlight color cells\", value: \"#F5F5DC\"})","pinned":false,"hidden":false,"mode":"ojs"}],"files":"$W31","stdlib":"1","titling":"auto"}