Unit 8: The NormalDistributionEx 1: P(0) = .9, P(1) = .1n = 1, 3, 10, 25, 400After n draws, the possible sumsare 0 to n, but the most proba-ble sums group close to .1n.Same initial distribution aslast slide, but with horizon-tal scale adjusted so thatthe possible range of out-comes, 0 to n , is alwaysthe same width.The next slide is similar,with two other initial dis-tributions, both from thetext.Ex: Law of Averages + Central Limit TheoremRoll a die n times, with n = 6, 12, 24, 48, 96. What are theprobabilities of getting exactly k 4’s?On edstat-l usenet discussion group:From: IN%"wvenableOa attunga.stats.adelaide.edu.au" 20-JAN-199508:59:13.14Subj: RE: Internet-Based Survey ResearchIf you mean "surveys" of the kind where someone puts an articlein several newsgroups asking people to fill out an electronicquestionnaire and return it, the answer has always seemed to meto be simple: Such surveys are ALWAYS a waste of time andresources since they can only yield non-random, indeedself-selected samples from an ill-defined population. Theprocedure is on exactly the same footing as TV telephone polls,newspaper advertisement polls and the like. The procedure doesnot to stand up to the most basic scientific criteria of validityand thus the exercise is futile for any formal academic purpose(except, perhaps, journalism). They should be outlawed andattract very serious penalties on the grounds that they are avery blatant abuse of the internet. No offence intended . . .Bill Venables, Department of Statistics, The University ofAdelaide, South AUSTRALIA. 5005.Sample survey: Randomize!Simple random sample!Ievery sample of given size has same chance of being chosenItheory is based on randomnessCluster random sample?Ipick some “clusters” out of population and poll everyone inthemIsmall samples (and there are fewer clusters than individuals)means less randomnessStratified random sample?Idivide entire population into “strata” and take random sampleof each stratumIif strata are not of equal size, small ones may beover-represented in