Let MX(t) and MY(t) be the moment generating functions of two random variables X and Y respectively, for some t in R. If E(X) = 1/2, Var(X) = 1/4 and MY(t) = (0cdot 75 + 0cdot 25e^2t)MX(t), where t in (-h, h); h 0, then what is Var(Y) equal to?

Q9Section I (Objective (Q1–Q80))9 of 80

Distribution Theory — variance from factorised mgf

Let $M_X(t)$ and $M_Y(t)$ be the moment generating functions of two random variables $X$ and $Y$ respectively, for some $t \in \mathbb{R}$ . If $\mathbb{E}(X) = \frac{1}{2}$ , $\operatorname{Var}(X) = \frac{1}{4}$ and $M_Y(t) = (0\cdot 75 + 0\cdot 25e^{2t})M_X(t)$ , where $t \in (-h, h)$ ; $h > 0$ , then what is $\operatorname{Var}(Y)$ equal to?

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