Consider two random variables, X and Y. Let E(X) and E(Y) denote the population means of...

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Answer 1

Answer #1

Given that, population mean and population variance of X and Y are, E(X) , E(Y) and Var(X), Var(Y)

Let Z = 3X - Y

Assume that X and Y are independent, so Cov(X, Y) = 0

We want to find, the Variance of Z,

Var(Z)

= Var ( 3X - Y)

= Var(3X) + Var(Y) - 2 * 3 * Cov(X,Y)

= 3² * Var(X) + Var(Y) - 0

= 9 * Var(X) + Var(Y)

Therefore,

Var(Z) = 9 * Var(X) + Var(Y)

Answer 2

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