29:null 2a:["$","title",null,{"children":"Edge cases | Andy Bloch | Observable"}] 2f:[] 2d:{"id":"6f6a0a4fd520f6e2","slug":null,"title":"Edge cases","thumbnail":"14f3e216e045ec2f5b1d488be915f953bfab807f7bdc9162ca686a178322e00a","access_level":"public","create_time":"$D2023-11-11T01:02:48.573Z","update_time":"$D2024-09-28T20:25:56.625Z","view_time":null,"first_public_time":"$D2023-11-11T01:02:48.573Z","fork":false,"stars":2,"starred":false,"owner":{"type":"team","id":"1f31ae6127750b50","login":"andy-bloch","name":"Andy Bloch","avatar_url":"https://avatars-next.observableusercontent.com/f8d4001bdab27a3cfa956d8e8ce42e845944efa3f199456264dad93d7d00a47a","tier":"starter_2024"},"version":233,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"32eb0f53cf971b80","login":"andy-bloch","name":"Andy Bloch","avatar_url":"https://avatars-next.observableusercontent.com/f8d4001bdab27a3cfa956d8e8ce42e845944efa3f199456264dad93d7d00a47a","tier":null}],"members":[{"type":"individual","id":"32eb0f53cf971b80","login":"andy-bloch","name":"Andy Bloch","avatar_url":"https://avatars-next.observableusercontent.com/f8d4001bdab27a3cfa956d8e8ce42e845944efa3f199456264dad93d7d00a47a","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"subscribed":null,"forks":1,"collection":null,"type":"notebook","body":{"title":"Edge cases","cells":[{"id":0,"value":"# Edge cases","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined"},{"id":5,"value":"https://twitter.com/natesilver538/status/1723130769751548005?s=12&t=1NKp0OrOc6CLmNw7Jlf23A\n\n

Nate Silver

\n@NateSilver538

\n\n> Free speech is about the edge cases. You don't have to be an absolutist, like if you go with free speech in 80% of the edge cases but think 20% are beyond the pale, OK whatever. But if you don't favor free speech in *any* of the edge cases, you don't believe in free speech.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined"},{"id":176,"value":"Justices go with free speech in 50% of the edge cases.\n\nJustices vote with the majority in 50% of the edge cases (if their opinions are independent of each other).","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined"},{"id":124,"value":"{\n let data = [];\n for (let pi = 0 ; pi <= 1000 ; pi++) {\n let p = pi/1000;\n for (let k = 0 ; k < 9; k++) {\n let d = {\n p,\n k,\n cum: 1-binomialCum(k,9,p)\n };\n data.push(d);\n }\n }\n return Plot.plot({\n width: 400,\n color: {\n legend: true,\n },\n aspectRatio: 1,\n x: {\n grid: true,\n },\n y: {\n grid: true,\n },\n marks: [\n Plot.ruleX([0.5]),\n Plot.ruleY([0.5]), \n Plot.line(data, {\n strokeWidth: 3,\n stroke: d=>d.k,\n x: \"p\",\n y: \"cum\"\n }),\n ]\n });\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":45,"value":"factorial = {\n const r=[1,1];\n return function f(n) {\n return r[n] || (n < 0 ? 0 : (r[n] = n*f(n-1)));\n }\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":180,"value":"choose = {\n function f(n, k) {\n if (k <= 0 || k >= n) {\n return 1;\n }\n let s = \"\" + n + \"c\" + k;\n \n return f.mem[s] || (f.mem[s] = Math.round((n-k+1) / k * f(n,k-1)));\n }\n f.mem = {};\n return f;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":195,"value":"choose.mem","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":189,"value":"choose2(100,12)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":185,"value":"choose(100,12)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":49,"value":"function choose2(n,k) {\n return factorial(n)/ factorial(k)/factorial(n-k);\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":63,"value":"function binomial(k,n,p) {\n return choose(n,k)*Math.pow(p,k)*(Math.pow(1-p,n-k));\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":116,"value":"function binomialCum(k,n,p) {\n let c = binomial(k,n,p);\n if (k >= 1) {\n c += binomialCum(k-1,n,p);\n }\n return c;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":68,"value":"function generatePMF(n,p) {\n return Array.from({length:n}).map((_,k)=>({k,binomial:binomial(k,n,p)}));\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":73,"value":"pmf = generatePMF(9,0.25)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":99,"value":"Plot.plot({\n y: {\n grid: true,\n },\n marks: [\n Plot.barY(pmf, { x: \"k\", y: d=>binomialCum(d.k,9,0.1), tip: true }),\n //Plot.barY(pmf, Plot.mapY(\"cumsum\", {x: \"k\", y: \"bernoulli\"})),\n ]\n})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":136,"value":"build_samples(p=>binomialCum(4,9,p),0,1)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":131,"value":"https://observablehq.com/@mcmcclur/plot-for-mathematicians","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined"},{"id":128,"value":"import { build_samples } from '@mcmcclur/adaptive-plotter'\n","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"}],"files":"$W2f","stdlib":"1","titling":"auto"}} 2e:"$2d:body"