Q3. Suppose that X is a Gamma distributed random variable with parameters a and 2. Additionally, Y is uniform on [0,1] and that X and Y are independent. a) Compute the variance of Z = XY. b) Compute the moment generating function (mgf) of W = X + Y.

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Q3. Suppose that ? is a Gamma distributed random variable with parameters ? and ?.
Additionally, ? is uniform on [0,1] and that ? and ? are independent.
a) Compute the variance of ? = ??.
b) Compute the moment generating function (mgf) of ? = ? + ?.

Q3. Suppose that X is a Gamma distributed random variable with parameters a and 2.
Additionally, Y is uniform on [0,1] and that X and Y are independent.
a) Compute the variance of Z = XY.
b) Compute the moment generating function (mgf) of W = X+ Y.
Transcribed Image Text:Q3. Suppose that X is a Gamma distributed random variable with parameters a and 2. Additionally, Y is uniform on [0,1] and that X and Y are independent. a) Compute the variance of Z = XY. b) Compute the moment generating function (mgf) of W = X+ Y.
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