Question

Let the moment generating function (m.g.f) of a random variable is of the form \(M_X(t)=(0.4e^t +0.6)^8\). Find the mean and variance of a random variable Y=3X+2.

• A. E(Y) =9.4 and V(Y) = 17.28
• B. E(Y) =9.6 and V(Y) = 17.26
• C. E(Y) =9.4 and V(Y) = 17.26
• D. E(Y) =9.6 and V(Y) = 17.28

Hint:

When applying linear transformations to variance, always square the multiplier:
\[ V(aX + b) = a^2 V(X) \]
Since \(a = 3\), the variance must be multiplied by \(9\).
\[ 9 \times 1.92 = 17.28 \]
This immediately eliminates options (B) and (C).

Answer 1

The Correct Option is D