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Feb 12 Lecture.doc

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Political Science
Kenichi Ariga

Feb 12 Lecture February-12-14 6:01 PM Probability and Probability Distribution: Big Picture: Stat inference • Cannot study everyone in population so must take a sample (random). • Probability: random frequency • Random Sample, define probability of observing certain characteristics. Repeated sampling from the same population ie. * Rolling the die example* • Probability is= proportion of times you can observe a characteristics from repeated sampling from the same population (Long run relative frequency) Probability: example • 1 bucket and 3 different plastic ducks (after the model of Canadian voters) • A girl is drawing a duck from the basket, and she wants the princess duck. What is the probability of her pulling this duck? 1/3 • 1/(1+1+1)=1/3 * # desired duck (numerator)/ # ducks in total • =0.3333 or 33.33% • now 2 yellow duckies, 1 purple, 1 princess • 1/ (2+1+1)=1/4 = 0.25 Canadian Federal Election 2011 • The probability of observing a certain characteristic equals the proportion of individuals in the population who have voted for the conservatives • We can compute this because we know the population distribution • In real life we do not know the actual distribution of the population • Therefore we need to make inference based on random sample. Conditional Probability • We use Pr (ElF) • Ex. Chance of rain in the next hour given the current look of sky PR (RainlBlue Sky) • Chance of rain around that time was 10% • But if sky changes, prob of rain increases • Chance of rain is always the conditional probability Duckie Ex. What is the probability that she will get a princess duckie given that it was not a yellow duckie : PR(ply) = 1/ (1+1)=0.5 = 50% • Eliminate the unwanted duck and compute only the amount of desired duck and total amount of ducks Canadian Federal Election 2011 • What is the conditional prob. that a randomly drawn individual will vote for conservative considering that he or she has cast the ballot = 1/16 US Presidential Election 2012 • V&D- voted for democratic • V&R-voted for republic • A- abstained from voting Rule 1: Pr (not E)= 1-PrE
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