2a:null 2b:["$","title",null,{"children":"Poissonfördelning | Mattias Villani | Observable"}] 31:[] 2e:{"id":"ead37e06dd3cddac","slug":"poissonfordelning","title":"Poissonfördelning","thumbnail":"df6b7ea2f1799dcdb1385eb99b3d037ff78abe26d59a61244ded36e55be74731","access_level":"public","create_time":"$D2023-01-31T17:32:32.726Z","update_time":"$D2023-11-17T20:58:34.678Z","view_time":null,"first_public_time":"$D2023-01-31T17:32:32.726Z","fork":{"id":"15db2285aae0bfdd","slug":"geometrisk-fordelning","title":"Geometrisk fördelning","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":782,"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":3,"collection":{"id":"209e13808f44ed11","slug":"sda1","title":"SDA1","owner":{"id":"7592a7ab121f74a0","login":"mattiasvillani","name":"Mattias Villani"}},"type":"notebook","body":{"title":"Poissonfördelning","cells":[{"id":38,"value":"# Poissonfördelning","pinned":false,"hidden":false,"mode":"md"},{"id":758,"value":">

${tex`X\\sim \\operatorname{Poisson}(\\lambda)`}, för ${tex`X \\in \\{0,1,2,\\ldots,\\}`}","pinned":false,"hidden":false,"mode":"md"},{"id":496,"value":"## Sannolikhetsfunktion och moment","pinned":false,"hidden":false,"mode":"md"},{"id":118,"value":"viewof params = Inputs.form([\n Inputs.range([0.1, 10], {value: 2, step: 0.1, label: tex`\\lambda:`}),\n Inputs.range([1, 10], {value: 1, step: 1, label: \"Kvantil:\"})\n ])","pinned":false,"hidden":false,"mode":"ojs"},{"id":461,"value":"dist_quantile = tex`\\text{Om } X \\sim \\operatorname{Poisson}(${params[0]}) \\text{ så gäller att } `","pinned":false,"hidden":false,"mode":"ojs"},{"id":555,"value":"moments = tex`\n\\begin{aligned}\n&E( X) = \\lambda = ${params[0].toPrecision(3)} \\\\[1em]\n&Var( X) = \\lambda = ${params[0].toPrecision(3)} \\\\[1em]\n&P( X\\leq ${params[1]}) =${poiscdf.toPrecision(4)}\n\\end{aligned}\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":305,"value":"plt_pdf = Plot.plot({\n color: { \n legend: false\n },\n x: {\n label: \"x\",\n axis: true\n },\n y: {\n label: \"f(x)\",\n axis: true\n },\n tooltip: {\n fill: \"#355E3B\",\n stroke: \"#355E3B\",\n opacity: 1,\n },\n marks: [\n Plot.ruleY([0]),\n Plot.barY(poispdf,{x: \"x\", y: \"pdf\", fill: \"#C1E1C1\", strokeWidth: 0, opacity: 1,\n title: (d) => `P(X=${d.x}) = ${(d.pdf).toPrecision(4)}`}),\n Plot.barY(poispdf, {filter: d => d.x <= params[1], x: \"x\", y: \"pdf\", fill: \"#228B22\", opacity: 1,\n title: (d) => `P(X=${d.x}) = ${(d.pdf).toPrecision(4)}`})\n ]\n })","pinned":false,"hidden":false,"mode":"ojs"},{"id":109,"value":"
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n\n---\n## 🙈 Appendix 🙈\n\nHär följer bara kod och detaljer som du antagligen inte vill läsa.","pinned":false,"hidden":false,"mode":"md"},{"id":221,"value":"#### Imports","pinned":false,"hidden":false,"mode":"md"},{"id":26,"value":"jstat = require('jstat')","pinned":false,"hidden":false,"mode":"ojs"},{"id":761,"value":"import {Plot} from \"@mkfreeman/plot-tooltip\"","pinned":true,"hidden":false,"mode":"ojs"},{"id":223,"value":"#### Data","pinned":false,"hidden":false,"mode":"md"},{"id":17,"value":"poispdf = {\n const x = d3.range(0, params[0] + 4*Math.sqrt(params[0]), 1);\n const data = x.map(x => ({x: x, pdf: jstat.poisson.pdf(x, params[0])}));\n return data\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":19,"value":"poiscdf = jstat.poisson.cdf(params[1], params[0]);","pinned":false,"hidden":false,"mode":"ojs"},{"id":229,"value":"#### Style","pinned":false,"hidden":false,"mode":"md"},{"id":202,"value":"","pinned":false,"hidden":false,"mode":"html"},{"id":58,"value":"viewof md_colour = Inputs.color({label: \"Highlight color cells\", value: \"#F5F5DC\"})","pinned":false,"hidden":false,"mode":"ojs"}],"files":"$W31","stdlib":"1","titling":"auto"}} 2f:"$2e:body"