Unformatted text preview: minutes. Thus, the birth minutes of diﬀerent people are independent discrete–uniform random variables on the set { 1 , 2 , 3 ,... , 525 , 600 } . About how many people do you need in a room to have a 50–50 chance (that is, probability 1 2 ) of there being at least one birth minute shared by two or more people? 4. Let X and Y be independent U [0 , 1] random variables. Find the density of Z =Y/ ln( X ). 5. Let N be geometric ( p ), with P { N = k } = (1p ) k1 p, k = 1 , 2 ,... , EN = 1 p , var( N ) = q p 2 . Let X 1 ,X 2 ,... be independent unit–exponential random variables, with density f ( x ) = ex , x > 0, and EX n = var( X n ) = 1. The X n ’s are independent of N . Let Y = N X i =1 X i . Find the variance of Y ....
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 Spring '09
 Probability, Variance, Probability theory, probability density function, black beads

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