Answer to Question #86837 in Statistics and Probability for Anand

Question

If a random variable X₁ has mean 4 and variance 9, while the random variable X₂
has mean − 2and variance 5, and the two are independent, find
i) E(2X₁ + X₂ - 5)
ii) Var(2X₁ + X₂ - 5)

Answer 1

$$E(X_1)=4, Var(X_1)=9, E(X_2)=-2, Var(X_2)=5.$$

$$i) E(2X_1+X_2-5)=2E(X_1)+E(X_2)-5=2*4-2-5=1$$

ii) If X₁ and X₂ are independent then

$$Var(2X_1+X_2-5)=2^2Var(X_1)+Var(X_2)=4*9+5=41$$