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Unformatted text preview: STAT 333 Assignment 2 Due: Thursday, Nov. 4 at the beginning of the class (Please print) Last name: First Name: ID#: Acknowledgements: Mark: TA’s initials: 1. let X i ,i = 1 , 2 ,...n , are i.i.d. random variables with uniform distributions on [0 , 1], where n is a positive integer. (1) Find P r ( X 1 ≤ X 2 ) or P r ( X 1 = min ( X 1 ,X 2 )). (2) Find P r ( X 1 ≤ X 2 ,X 1 ≤ X 3 ) or P r ( X 1 = min ( X 1 ,X 2 ,X 3 )). (3) Find P r ( X 1 ≤ X 2 ,X 1 ≤ X 3 ,...,X 1 ≤ X n ) or P r ( X 1 = min ( X 1 ,X 2 ,X 3 ,...,X n )). 2. (#27 chapter 3) A coin that comes up heads with probability p, < p < 1, is continually flipped until the pattern T,T,H appears. (That is, you stop flipping when the most recent flip lands heads, and the two immediately preceding it lands tails). Let X denote the number of flips made, and find E(X). 3. (#37 chapter 3) A manuscript is sent to a typing firm consisting of typists A , B , and C . If it is typed by A then the number of errors made is Poisson random variable with mean 2.6; If typed by B , then the number of errors is a Poisson random variable with mean 3;...
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 Fall '10
 MenZhongxian
 Probability, Probability theory, renewal event, delayed renewal event, renewal sequence, associated renewal sequence

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