2a:null 2b:["$","title",null,{"children":"Exponentialfördelningen | Mattias Villani | Observable"}] 31:[] 2e:{"id":"25d835ea95563034","slug":"exponentialfordelningen","title":"Exponentialfördelningen","thumbnail":"54cd2153bd14deb7973073fe821f55b7b40bca080d4b494e726fa83545c4ddad","access_level":"public","create_time":"$D2023-01-31T12:49:52.560Z","update_time":"$D2023-11-17T20:57:26.238Z","view_time":null,"first_public_time":"$D2023-01-31T12:49:52.560Z","fork":{"id":"32c30160ed8888fa","slug":"normalfordelningen","title":"Normalfördelningen","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":588,"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":"209e13808f44ed11","slug":"sda1","title":"SDA1","owner":{"id":"7592a7ab121f74a0","login":"mattiasvillani","name":"Mattias Villani"}},"type":"notebook","body":{"title":"Exponentialfördelningen","cells":[{"id":38,"value":"# Exponentialfördelningen","pinned":false,"hidden":false,"mode":"md"},{"id":586,"value":">

${tex`X\\sim \\operatorname{Expon}(\\lambda)`}, för ${tex`X >0`}","pinned":false,"hidden":false,"mode":"md"},{"id":496,"value":"## Sannolikhetsfunktion och moment","pinned":false,"hidden":false,"mode":"md"},{"id":118,"value":"viewof params = Inputs.form([\n Inputs.range([0.01, 10], {value: 1, step: 0.1, label: tex`\\lambda:`}),\n Inputs.range([0.01, 10], {value: 1, step: 0.01, label: \"Kvantil:\"})\n ])","pinned":false,"hidden":false,"mode":"ojs"},{"id":461,"value":"dist_quantile = tex`\\text{Om } X \\sim \\operatorname{Expon}(${params[0]}) \\text{ så gäller att } `","pinned":false,"hidden":false,"mode":"ojs"},{"id":555,"value":"moments = tex`\n\\begin{aligned}\n&E( X) =\\frac{1}{\\lambda} = ${(1/params[0]).toPrecision(3)} \\\\[1em]\n&Var( X) =\\frac{1}{\\lambda^2} = ${(1/params[0]**2).toPrecision(3)} \\\\[1em]\n&P( X\\leq ${params[1]}) =${exponcdf.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.exponential.pdf(0, params[0])]\n },\n marks: [\n Plot.ruleY([0]),\n Plot.ruleX([0]),\n Plot.line(exponpdf, {x: \"x\", y: \"pdf\", stroke : \"orange\", strokeWidth: 2}),\n Plot.areaY(exponpdf, {filter: d => d.x <= params[1], x: \"x\", y: \"pdf\", fill: \"orange\", 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":"exponpdf = {\n const x = d3.range(0.01, 5, 0.01);\n const exponpdf = x.map(x => ({x: x, pdf: jstat.exponential.pdf(x, params[0])}));\n return exponpdf\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":19,"value":"exponcdf = jstat.exponential.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"