X and Y are two independent random variables. X has an exponential distribution with E (X)...
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X and Y are two independent random variables. X has an exponential distribution with E (X) = 2 and Y has an exponential distribution with E (Y) = 1. Another random variable Z is related to X and Y, such that Z = X + 2Y. i. Find the variance of Z. (4 marks) ii. Find the moment generating function of Z. Determine the distribution name of Z and its parameter? (7 marks) X and Y are two independent random variables. X has an exponential distribution with E (X) = 2 and Y has an exponential distribution with E (Y) = 1. Another random variable Z is related to X and Y, such that Z = X + 2Y. i. Find the variance of Z. (4 marks) ii. Find the moment generating function of Z. Determine the distribution name of Z and its parameter? (7 marks)
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Z is the normal distribution with mean4 Variance8 A detailed solution atta... View the full answer
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