ams572_notes_1

ams572_notes_1 - AMS 572 Lecture Notes #1 Sep. 3rd, 2010...

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AMS 572 Lecture Notes #1 Sep. 3 rd , 2010 Review Probability: Eg. 1. Suppose each child’s birth will result in either a boy or a girl with equal probability. For a randomly selected family with 2 children, what is the chance that the chosen family has 1) 2 boys? 2) 2 girls? 3) a boy and a girl? Solution: 25%; 25%; 50% P(B and B)= P(B∩B)= P(B)∙P(B)=0.5∙0.5=0.25 P(G and G)= P(G∩G)= P(G)∙P(G)=0.5∙0.5=0.25 P(B and G)= or = Binomial Experiment: 1) It consists of n trials 2) Each trial results in 1 of 2 possible outcomes, “S” or “F” 3) The probability of getting a certain outcome, say “S”, remains the same, from trial to trial, say P(“S”)=p 4) These trials are independent, that is the outcomes from the previous trials will not affect the outcomes of the up-coming trials Eg. 1 (continued) n=2, let “S”=B, P(B)=0.5 Let X denotes the total # of “S” among the n trials then X~B(n, p) Its probability density function (pdf) is , x=0,1,…,n **For a discrete random variable, its pdf is also called its probability mass function (pmf) 1
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ams572_notes_1 - AMS 572 Lecture Notes #1 Sep. 3rd, 2010...

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