30:[] 2e:{"title":"Expectation","cells":[{"id":0,"value":"md`# Expectation`","pinned":false,"hidden":false,"mode":"ojs"},{"id":39,"value":"html`

Flipping a Coin

`","pinned":false,"hidden":false,"mode":"ojs"},{"id":42,"value":"html`A coin is flipped once. Let X be 0 if tails shows, 1 if heads shows. What is the expectation of X?`","pinned":false,"hidden":false,"mode":"ojs"},{"id":47,"value":"tex`E(X) = \\text{ }?`","pinned":false,"hidden":false,"mode":"ojs"},{"id":131,"value":"{\n const x = [0,1]\n const p = [.5,.5]\n return math.dot(x,p)\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":57,"value":"html`

Flipping Two Coins

`","pinned":false,"hidden":false,"mode":"ojs"},{"id":60,"value":"html`Two coins are flipped. If a head shows, record that as a 1. If a tail shows, record that as a 0. Let X be the sum of the two outcomes.`","pinned":false,"hidden":false,"mode":"ojs"},{"id":64,"value":"tex`E(X) = \\text{ }?`","pinned":false,"hidden":false,"mode":"ojs"},{"id":135,"value":"{\n const x = [0,1,2]\n const p = [.25,.5,.25]\n return math.dot(x,p)\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":139,"value":"tex`E(X^{2}) = \\text{ }?`","pinned":false,"hidden":false,"mode":"ojs"},{"id":144,"value":"{\n const x = [0,1,4]\n const p = [.25,.5,.25]\n return math.dot(x,p)\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":82,"value":"html`

Binomial

`","pinned":false,"hidden":false,"mode":"ojs"},{"id":85,"value":"html`You can make a shot from a particular spot on the basketball court with probability .6. You will take 4 shots. Let X be the number of times you make it. `","pinned":false,"hidden":false,"mode":"ojs"},{"id":90,"value":"tex`E(X) = \\text{ }?`","pinned":false,"hidden":false,"mode":"ojs"},{"id":149,"value":"math.combinations(4,4)*math.pow(.6,4)*math.pow(.4,0)","pinned":false,"hidden":false,"mode":"ojs"},{"id":152,"value":"{\n const x = [0,1,2,3,4]\n const p = [.0256,.1536,.3456,.3456,.1296]\n return math.dot(x,p)\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":93,"value":"html`

Two Four-Sided Dice

`","pinned":false,"hidden":false,"mode":"ojs"},{"id":96,"value":"html`You roll two four-sided dice. Let X be the sum of the results.`","pinned":false,"hidden":false,"mode":"ojs"},{"id":165,"value":"{\n const outcomes = []\n for(let i = 1;i<=4;i = i + 1){\n for(let j = 1;j<=4;j = j + 1){\n outcomes.push({die1:i,die2:j,sum:i + j})\n }\n }\n return outcomes\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":99,"value":"tex`E(X) = \\text{ }?`","pinned":false,"hidden":false,"mode":"ojs"},{"id":169,"value":"{\n const x = [2,3,4,5,6,7,8]\n const p = [1/16,2/16,3/16,4/16,3/16,2/16,1/16]\n return math.dot(x,p)\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":5,"value":"html`

Libraries

`","pinned":false,"hidden":false,"mode":"ojs"},{"id":7,"value":"d3 = require(\"d3@5\")","pinned":false,"hidden":false,"mode":"ojs"},{"id":9,"value":"import {slider,button,select,text,radio,checkbox,number} from \"@jashkenas/inputs\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":11,"value":"math = require('mathjs@6.2.1/dist/math.js')","pinned":false,"hidden":false,"mode":"ojs"},{"id":13,"value":"stat = require('simple-statistics@7.3.0/dist/simple-statistics.min.js')\n","pinned":false,"hidden":false,"mode":"ojs"},{"id":20,"value":"{\n const svg = html`` \n const container = d3.select(svg)\n container.attr(\"style\",\"width: 600px; height: 300px; border:1px black solid\")\n \n \n return svg\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":24,"value":"makeXAxis = function(container,domain,range,y,ticks){\n const xScale = d3.scaleLinear().domain(domain).range(range)\n const xAxis = container.append(\"g\").attr(\"transform\",`translate(0,${y})`)\n d3.axisBottom(xScale).ticks(ticks)(xAxis)\n return xScale\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":27,"value":"makeYAxis = function(container,domain,range,x,ticks){\n const yScale = d3.scaleLinear().domain(domain).range(range)\n const yAxis = container.append(\"g\").attr(\"transform\",`translate(${x},0)`)\n d3.axisLeft(yScale).ticks(ticks)(yAxis)\n return yScale\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":33,"value":"makeBar = function(container,xScale,yScale,x,p,width,fill,opacity){\n container.append(\"rect\")\n .attr(\"x\",xScale(x - width))\n .attr(\"y\",yScale(p))\n .attr(\"width\",xScale(x + width)- xScale(x - width))\n .attr(\"height\",yScale(0) - yScale(p))\n .attr(\"fill\",fill)\n .attr(\"stroke\",\"black\")\n .attr(\"opacity\",opacity)\n\n}","pinned":false,"hidden":false,"mode":"ojs"}],"files":"$W30","stdlib":"1","titling":"auto"}