2a:null 2b:["$","title",null,{"children":"Beta-fördelningen | Mattias Villani | Observable"}] 31:[] 2e:{"id":"04eba2cc11169bfb","slug":"beta-fordelningen","title":"Beta-fördelningen","thumbnail":"87f6d922989cfe72ad7f2fe6770e6a39fddbf476e6dcc7cf6d730cfefb85f2dc","access_level":"public","create_time":"$D2023-01-31T21:35:14.916Z","update_time":"$D2023-11-17T20:57:39.085Z","view_time":null,"first_public_time":"$D2023-01-31T21:35:14.916Z","fork":{"id":"1b150f86eb91a63a","slug":"chi2-fordelningen","title":"Chi2-fördelningen","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":660,"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":1,"collection":{"id":"209e13808f44ed11","slug":"sda1","title":"SDA1","owner":{"id":"7592a7ab121f74a0","login":"mattiasvillani","name":"Mattias Villani"}},"type":"notebook","body":{"title":"Beta-fördelningen","cells":[{"id":38,"value":"# Beta-fördelningen","pinned":false,"hidden":false,"mode":"md"},{"id":656,"value":">

${tex`X\\sim \\operatorname{Beta}(\\alpha,\\beta)`}, för ${tex`X \\in (0,1)`}","pinned":false,"hidden":false,"mode":"md"},{"id":496,"value":"## Sannolikhetsfunktion och moment","pinned":false,"hidden":false,"mode":"md"},{"id":118,"value":"viewof params = Inputs.form([\n Inputs.range([0.1, 20], {value: 3, step: 0.1, label: tex`\\alpha`}),\n Inputs.range([0.1, 20], {value: 3, step: 0.1, label: tex`\\beta`}),\n Inputs.range([0, 1], {value: 0.2, step: 0.01, label: \"Kvantil:\"})\n ])","pinned":false,"hidden":false,"mode":"ojs"},{"id":461,"value":"dist_quantile = tex`\\text{Om } X \\sim \\operatorname{Beta}(${params[0]},${params[1]}) \\text{ så gäller att } `","pinned":false,"hidden":false,"mode":"ojs"},{"id":555,"value":"moments = tex`\n\\begin{aligned}\n&E( X) =\\frac{\\alpha}{\\alpha + \\beta} = ${(params[0]/(params[0] + params[1])).toPrecision(2)} \\\\[1em]\n&Var( X) = \\frac{\\alpha \\beta}{(\\alpha + \\beta)^2(\\alpha + \\beta + 1)} = ${((params[0]*params[1])/((params[0] + params[1])^2*(params[0] + params[1] +1 ))).toPrecision(2)} \\\\[1em]\n&P( X\\leq ${params[2]}) =${betacdf.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 },\n y: {\n label: \"f(x)\",\n //axis: false,\n domain: [0,jstat.beta.pdf((params[0]-1)/(params[0]+params[1]-2), params[0], params[1])]\n },\n marks: [\n Plot.ruleY([0]),\n Plot.ruleX([0]),\n Plot.line(betapdf, {x: \"x\", y: \"pdf\", stroke : \"red\", strokeWidth: 2}),\n Plot.areaY(betapdf, {filter: d => d.x <= params[2], x: \"x\", y: \"pdf\", fill: \"red\", opacity: 0.2})\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":223,"value":"#### Data","pinned":false,"hidden":false,"mode":"md"},{"id":17,"value":"betapdf = {\n const x = d3.range(0, 1.01, 0.01);\n const pdf = x.map(x => ({x: x, pdf: jstat.beta.pdf(x, params[0], params[1])}));\n return pdf\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":19,"value":"betacdf = jstat.beta.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"}} 2f:"$2e:body"