Question: Q3 thank you distributed with parameter 9. What is the conditional distribution for X given that X + Y = n? 3. (Problem 2.3.4 in

Q3 thank you

distributed with parameter 9. What is the conditional distribution for X given that X + Y = n? 3. (Problem 2.3.4 in Pinsky and Karlin) Suppose 61,52, . .. are independent and identically distributed random variables having mean y. and variance 02. Form the random sum SN = {1 + - - . + EN. (a) Derive the mean and variance of SN When N has a Poisson distribution with parameter A. (1)) Determine the mean and variance of SN when N has a geometric distribution with mean A = (1 p)/p. (c) Compare the behaviours in the above two questions as A > oo

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