2a:null 2b:["$","title",null,{"children":"Binomial distribution | Mattias Villani | Observable"}] 31:[] 2e:{"id":"8e97614a2bda7e05","slug":"binomial-distribution","title":"Binomial distribution","thumbnail":"30c6efce3f2d579f1cc397d39eb000413518c3aa576ce4c2715a04d5f2117c29","access_level":"public","create_time":"$D2023-02-10T10:44:05.202Z","update_time":"$D2024-01-02T10:48:03.219Z","view_time":null,"first_public_time":"$D2023-02-10T10:44:05.202Z","fork":{"id":"d0c90564be03f922","slug":"binomialfordelningen","title":"Binomialfördelningen","owner":{"id":"7592a7ab121f74a0","login":"mattiasvillani","name":"Mattias Villani"}},"stars":0,"starred":false,"owner":{"type":"team","id":"7592a7ab121f74a0","login":"mattiasvillani","name":"Mattias Villani","avatar_url":"https://avatars-next.observableusercontent.com/a440aaf39a3abefb86cbcc758fd7a5ab42555ae68d6825b52ec006f385a94d1d","tier":"pro_2024"},"version":918,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"56499be8cf43f0ef","login":"mattiasvillani","name":"Mattias Villani","avatar_url":"https://avatars-next.observableusercontent.com/a440aaf39a3abefb86cbcc758fd7a5ab42555ae68d6825b52ec006f385a94d1d","tier":null}],"members":[{"type":"individual","id":"56499be8cf43f0ef","login":"mattiasvillani","name":"Mattias Villani","avatar_url":"https://avatars-next.observableusercontent.com/a440aaf39a3abefb86cbcc758fd7a5ab42555ae68d6825b52ec006f385a94d1d","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"subscribed":null,"forks":4,"collection":{"id":"40c8ef5af1a51aff","slug":"distributions","title":"Statistical distributions","owner":{"id":"7592a7ab121f74a0","login":"mattiasvillani","name":"Mattias Villani"}},"type":"notebook","body":{"title":"Binomial distribution","cells":[{"id":38,"value":"# Binomial distribution","pinned":false,"hidden":false,"mode":"md"},{"id":824,"value":"textdist = md`

${tex`X\\sim \\operatorname{Binom}(n,p)`}, for ${tex`X \\in \\{0,1,\\ldots,n\\}`}`","pinned":false,"hidden":false,"mode":"ojs"},{"id":496,"value":"### Probability function and moments","pinned":false,"hidden":false,"mode":"md"},{"id":118,"value":"viewof params = Inputs.form([\n Inputs.range([1, 200], {value: 10, step: 1, label: tex`n`}),\n Inputs.range([0, 1], {value: 0.5, step: 0.01, label: tex`p`}),\n ])","pinned":false,"hidden":false,"mode":"ojs"},{"id":665,"value":"viewof kvantil = Inputs.range([1, params[0]], {value: 3, step: 1, label: \"quantile\"})","pinned":false,"hidden":false,"mode":"ojs"},{"id":669,"value":"viewof approx = Inputs.toggle({label: \"show normal approximation\", value: false})","pinned":false,"hidden":false,"mode":"ojs"},{"id":555,"value":"moments = tex`\n\\text{If } X \\sim \\operatorname{Binom}(${params[0]},${params[1]}) \\text{ then }\\\\[0.5em]\n\n\nE( X) =n p = ${(params[0]*params[1]).toPrecision(3)} \\\\[0.5em]\nVar( X) =n p (1-p) =${(params[0]*params[1]*(1-params[1])).toPrecision(3)} \n\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":722,"value":"cdfs = \n{\n var cdf;\n if (approx){\n cdf = tex`\n \\begin{array}{ll}\n \\text{Exact:} & P( X\\leq ${kvantil}) =${binomcdf.toPrecision(4)} \\\\[0.25em]\n \\text{Normal approx:} & P( X\\leq ${kvantil}) =${normalapproxcdf.toPrecision(4)} \\\\[0.25em]\n \\text{Normal approx - corr:} & P( X\\leq ${kvantil}) =${normalapproxcdf_corrected.toPrecision(4)}\n \\end{array}\n `}\n else{\n cdf = tex`\n \\begin{array}{ll}\n \\text{Exact:} & P( X\\leq ${kvantil}) =${binomcdf.toPrecision(4)}\n \\end{array}\n ` \n }\n return cdf;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":305,"value":"plt_pdf = Plot.plot({\n color: { \n legend: approx\n },\n x: {\n label: \"x\",\n axis: true,\n domain: d3.range(0, params[0]+1, 1)\n },\n y: {\n label: \"f(x)\",\n domain: [0,1.1*jstat.binomial.pdf(params[0]*params[1], params[0],params[1])]\n },\n tooltip: {\n fill: \"#C04000\",\n stroke: \"#C04000\",\n opacity: 1,\n },\n marks: [\n Plot.ruleY([0]),\n Plot.barY(binompdf,{filter: d => d.type == \"exact\", x: \"x\", y: \"pdf\", fill : \"orange\", strokeWidth: 0, opacity: 0.8, \n title: (d) => `P(X=${d.x}) = ${(d.pdf).toPrecision(4)}`}),\n Plot.barY(binompdf, {filter: d => d.type == \"exact\" && d.x <= kvantil, x: \"x\", y: \"pdf\", fill: \"darkorange\", opacity: 1,\n title: (d) => `P(X=${d.x}) = ${(d.pdf).toPrecision(4)}`}),\n Plot.line(normalapproxpdf, {filter: d => approx, x: \"x\", y: \"pdf\", stroke : \"steelblue\", strokeWidth: 2}) \n ]\n })","pinned":false,"hidden":false,"mode":"ojs"},{"id":109,"value":"
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\n\n---\n## 🙈 Appendix 🙈\n\nHär följer bara kod och detaljer som du antagligen inte vill läsa.","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":697,"value":"import {Plot} from \"@mkfreeman/plot-tooltip\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":223,"value":"#### Data","pinned":false,"hidden":false,"mode":"md"},{"id":17,"value":"binompdf = {\n const x = d3.range(0, params[0]+1, 1);\n const binompdf = x.map(x => ({x: x, pdf: jstat.binomial.pdf(x, params[0], params[1]), type: \"exact\"}));\n const normalapproxpdf = x.map(x => ({x: x, pdf: jstat.normal.pdf(x, params[0]*params[1], Math.sqrt(params[0]*params[1]*(1-params[1]))),type: \"approx\"}));\n const data = binompdf.concat(normalapproxpdf)\n return data\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":605,"value":"normalapproxpdf = {\n const x = d3.range(0, params[0], 1);\n const normalapproxpdf = x.map(x => ({x: x, pdf: jstat.normal.pdf(x, params[0]*params[1], Math.sqrt(params[0]*params[1]*(1-params[1])))}));\n return normalapproxpdf\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":19,"value":"binomcdf = jstat.binomial.cdf(kvantil, params[0], params[1]);","pinned":false,"hidden":false,"mode":"ojs"},{"id":717,"value":"normalapproxcdf = jstat.normal.cdf(kvantil, params[0]*params[1], Math.sqrt(params[0]*params[1]*(1-params[1])))\n ","pinned":false,"hidden":false,"mode":"ojs"},{"id":753,"value":"normalapproxcdf_corrected = jstat.normal.cdf(kvantil+0.5, params[0]*params[1], Math.sqrt(params[0]*params[1]*(1-params[1])))\n","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"}} 2f:"$2e:body"