Q2Single correct3 Marks13 Apr 2025

If $X \sim \text{Exp}(\lambda)$, then find the PDF of $Y = \sqrt{X}$.

A

$f_Y(y) = \begin{cases} 2\lambda y e^{-\lambda y^2}, & y > 0 \\ 0, & \text{otherwise} \end{cases}$

B

$f_Y(y) = \begin{cases} \lambda e^{-\lambda y}, & y > 0 \\ 0, & \text{otherwise} \end{cases}$

C

$f_Y(y) = \begin{cases} \lambda e^{-\frac{\lambda y^2}{2}}, & y > 0 \\ 0, & \text{otherwise} \end{cases}$

D

$f_Y(y) = \begin{cases} \lambda y e^{-\lambda y^2}, & y > 0 \\ 0, & \text{otherwise} \end{cases}$