Let X and Y be two independent random variables having moment-generating functions MX(t)=(3/4+1/4e^t)^3 and MY(t)=e^2(e^t-1) What is P[(X+Y)<2] equal to?

Q37Section I (Objective (Q1–Q80))37 of 79

Distribution Theory — probability from independent binomial-Poisson MGFs

Let $X$ and $Y$ be two independent random variables having moment-generating functions

$M_X(t)=\left(\frac{3}{4}+\frac{1}{4}e^t\right)^3 \text{ and } M_Y(t)=e^{2(e^t-1)}$

What is $P[(X+Y)<2]$ equal to?

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