Q7Single correct3 Marks28 Apr 2024

Let $X_1, X_2, X_3 \sim \text{i.i.d. } X$ and $X \sim \text{Uniform}\{-0.2, 0.2\}$. Define a new random variable $S = X_1 + X_2 + X_3$. Find the MGF (moment generating function) of $S$.

A

$\left(\frac{e^{-0.2\lambda} + e^{0.2\lambda}}{3}\right)^3$

B

$\left(\frac{e^{-0.5\lambda} + e^{0.5\lambda}}{2}\right)^3$

C

$\left(\frac{e^{-0.2\lambda} + e^{0.2\lambda}}{2}\right)^3$

D

$\left(\frac{e^{-0.5\lambda} + e^{0.5\lambda}}{3}\right)^2$