Q27Single correct3 Marks1 Dec 2024

Let $X_1,X_2,\ldots,X_{10}$ be i.i.d. random variables with common MGF $M_X(\lambda)$. Find the MGF of $\bar X$, where $\bar X=(X_1+\cdots+X_{10})/10$.

A

$M_X(\lambda/10)$

B

$(M_X(\lambda))^{10}$

C

$M_{\bar X}(\lambda/10)^{10}$

D

$(M_X(\lambda/10))^{10}$