Let X and Y be two independent random variables such that the moment generating functions of X and Y are MX(t)=e^3(e^t-1), tinR, and MY(t)=(frac12e^-3t+frac12e^3t)^2, tinR, respectively. Then which of the following statements are true?

Q108Section C (Part C)108 of 120

Moment generating functions — identifying two distributions

Let $X$ and $Y$ be two independent random variables such that the moment generating functions of $X$ and $Y$ are $M_X(t)=e^{3(e^{t}-1)}$ , $t\in\mathbb{R}$ , and $M_Y(t)=\left(\frac12e^{-3t}+\frac12e^{3t}\right)^2$ , $t\in\mathbb{R}$ , respectively. Then which of the following statements are true?

Multiple select: one or more options are correct. Select all of them, then submit — marks need the exact set.

Select every correct option, then submit.

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