Q7Single correct2 Marks10 Jul 2022

Consider a random variable $X$ with the following PMF. Find the moment generating function of $X$.

A

$M_X(\lambda)=\frac14e^{-3\lambda}+\frac18e^{-2\lambda}+\frac12e^{-3\lambda}$

B

$M_X(\lambda)=\frac18+\frac14e^\lambda+\frac18e^{2\lambda}+\frac12e^{2\lambda}$

C

$M_X(\lambda)=\frac18+\frac14e^\lambda+\frac18e^{2\lambda}+\frac12e^{3\lambda}$

D

$M_X(\lambda)=\frac18e^\lambda+\frac18e^{2\lambda}+\frac12e^{3\lambda}$