2f:[] 2d:{"title":"Edge cases","cells":[{"id":0,"value":"# Edge cases","pinned":false,"hidden":false,"mode":"md"},{"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"},{"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"},{"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"},{"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"},{"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"},{"id":195,"value":"choose.mem","pinned":true,"hidden":false,"mode":"ojs"},{"id":189,"value":"choose2(100,12)","pinned":true,"hidden":false,"mode":"ojs"},{"id":185,"value":"choose(100,12)","pinned":true,"hidden":false,"mode":"ojs"},{"id":49,"value":"function choose2(n,k) {\n return factorial(n)/ factorial(k)/factorial(n-k);\n}","pinned":true,"hidden":false,"mode":"ojs"},{"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"},{"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"},{"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"},{"id":73,"value":"pmf = generatePMF(9,0.25)","pinned":false,"hidden":false,"mode":"ojs"},{"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"},{"id":136,"value":"build_samples(p=>binomialCum(4,9,p),0,1)","pinned":true,"hidden":false,"mode":"ojs"},{"id":131,"value":"https://observablehq.com/@mcmcclur/plot-for-mathematicians","pinned":false,"hidden":false,"mode":"md"},{"id":128,"value":"import { build_samples } from '@mcmcclur/adaptive-plotter'\n","pinned":true,"hidden":false,"mode":"ojs"}],"files":"$W2f","stdlib":"1","titling":"auto"}