Let x alternative N um 8 sigma 3 Y alternative N um 5 Sig

Let x alternative N (um = 8, sigma = 3), Y alternative N (um = 5, Sigma = 2) be independent normal random variables. Another random variable A is defined as A = X - 2 Y. What can be determined about the distribution of A

Solution

As

A = X - 2Y

Then

u(A) = u(X) - 2 u(Y) = 8 - 2*5 = -2

Also,

sigma(A) = sqrt[sigma^(X) + 2^2 sigma^2(Y)] = sqrt(3^2 + (2^2)*(2^2)) = 5

Hence,

OPTION D: A~N(u = -2, sigma = 5) [ANSWER, D]