Unformatted text preview: that the ﬁrst to arrive has to wait no longer than 10 minutes. Exercise 4 Let X and Y be a random sample of from the exponential distribution with pdf f ( x ) = ex < x < ∞ Let U = X/Y and V = X + Y . Find the joint pdf of the couple ( U,V ). Are U and V independent? Exercise 5 Let X 1 ,X 2 ,...,X n be a random sample of size n with uniform distribution over (0 , 1). Find the pdf of Y = max( X 1 ,X 2 ,...,X n ). Find E ( Y ) ,V ar ( Y ) and M Y ( t ), the moment generating function of Y . good luck...
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 Spring '10
 VariousTeachers
 Statistics, Binomial, Probability, Probability theory, ........., #, 10 minutes, AMERICAN UNIVERSITY OF BEIRUT

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