Answer to Question #288163 in Statistics and Probability for negs

Question

Given that X and Y are independent random variables and E(X) = 4, E(Y) = 7, Var(X) = 3, Var(Y) = 6; find Var(5X - 6).

Answer 1

Solution:

Given, E(X) = 4, E(Y) = 7, Var(X) = 3, Var(Y) = 6

$Var(5X - 6)=25Var(X)$ $[\because Var[aX + b] = a^2Var(X)]$

$\Rightarrow Var(5X - 6)=25\times 3=75$