2b:null 2c:["$","title",null,{"children":"Geometrisk fördelning | Mattias Villani | Observable"}] 31:[] 2f:{"id":"15db2285aae0bfdd","slug":"geometrisk-fordelning","title":"Geometrisk fördelning","thumbnail":"5132b21fd8cb7b7752c5cb7b39868c5ae2b076848141204b722ee23dfbdbcfdd","access_level":"public","create_time":"$D2023-01-31T17:01:04.392Z","update_time":"$D2023-02-04T19:53:54.930Z","view_time":null,"first_public_time":"$D2023-01-31T17:01:04.392Z","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":779,"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":2,"collection":{"id":"209e13808f44ed11","slug":"sda1","title":"SDA1","owner":{"id":"7592a7ab121f74a0","login":"mattiasvillani","name":"Mattias Villani"}},"type":"notebook","body":{"title":"Geometrisk fördelning","cells":[{"id":38,"value":"# Geometrisk fördelning","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined"},{"id":776,"value":">

${tex`X\\sim \\operatorname{Geom}(p)`}, for ${tex`X \\in \\{1,2,\\ldots\\}`}","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined"},{"id":496,"value":"## Sannolikhetsfunktion och moment","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined"},{"id":118,"value":"viewof params = Inputs.form([\n Inputs.range([0, 1], {value: 0.5, step: 0.01, label: tex`p:`}),\n Inputs.range([1, 10], {value: 3, step: 1, label: \"Kvantil:\"})\n ])","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":461,"value":"dist_quantile = tex`\\text{Om } X \\sim \\operatorname{Geom}(${params[0]}) \\text{ så gäller att } `","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":555,"value":"moments = tex`\n\\begin{aligned}\n&E( X) = \\frac{1}{p} = ${(1/params[0]).toPrecision(3)} \\\\[1em]\n&Var( X) = \\frac{1-p}{p^2} =${((1-params[0])/(params[0]^2)).toPrecision(3)} \\\\[1em]\n&P( X\\leq ${params[1]}) =${geomcdf.toPrecision(4)}\n\\end{aligned}\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"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 title: \"titular\",\n tooltip: {\n fill: \"#0F52BA\",\n stroke: \"#0F52BA\",\n opacity: 1,\n },\n marks: [\n Plot.ruleY([0]),\n Plot.barY(geompdf,{x: \"x\", y: \"pdf\", fill: \"#B6D0E2\", strokeWidth: 0, opacity: 1,\n title: (d) => `P(X=${d.x}) = ${(d.pdf).toPrecision(4)}`}),\n Plot.barY(geompdf, {filter: d => d.x <= params[1], x: \"x\", y: \"pdf\", fill: \"#6F8FAF\", opacity: 1,\n title: (d) => `P(X=${d.x}) = ${(d.pdf).toPrecision(4)}`})\n ]\n })","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":109,"value":"
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\n\n---\n## 🙈 Appendix 🙈\n\nHär följer bara kod och detaljer som du antagligen inte vill läsa.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined"},{"id":221,"value":"#### Imports","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined"},{"id":26,"value":"jstat = require('jstat')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":223,"value":"#### Data","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined"},{"id":17,"value":"geompdf = {\n const x = d3.range(1, (1/params[0]) + 3*Math.sqrt(((1-params[0])/params[0]^2)), 1);\n const data = x.map(x => ({x: x, pdf: jstat.negbin.pdf(x-1, 1, params[0])}));\n return data\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":19,"value":"geomcdf = jstat.negbin.cdf(params[1]-1, 1, params[0]);","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":229,"value":"#### Style","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined"},{"id":202,"value":"","pinned":false,"hidden":false,"mode":"html","author":"$undefined","summary":"$undefined"},{"id":58,"value":"viewof md_colour = Inputs.color({label: \"Highlight color cells\", value: \"#F5F5DC\"})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":740,"value":"import {Plot} from \"@mkfreeman/plot-tooltip\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"}],"files":"$W31","stdlib":"1","titling":"auto"}} 30:"$2f:body"