January_2009_Common_Probabilty

January_2009_Common_Probabilty - , E[Y]=-2 , and Var (Y)=4....

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AMS Qualifying Examination, January 2009 Probability Questions 1. Bob tossed a symmetric coin ( n+1) times independently and counted the number of tails. John did the same n times. Compute the probability that Bob counted more tails than John. 2. Let (X,Y) be a bivariate random variable, where X is an exponential random variable with mean 1. Suppose that Cov (X,Y)=-2
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Unformatted text preview: , E[Y]=-2 , and Var (Y)=4. Find the cumulative distribution function of Y. 3. Let 3 2 1 , , X X X be three independent uniformly distributed random variables on [0,1]. Compute } { 2 1 3 X X X P . 4. Let X be a random variable with E[X]= and b X E 4 ) ( . Is it true that P{ | X- | t} b/t 4 ? Prove your answer....
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This note was uploaded on 01/31/2011 for the course AMS 507 taught by Professor Feinberg,e during the Fall '08 term at SUNY Stony Brook.

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