GATE ECE 1997 | Question 26

Question

Find the mean of a function $X(T)=\sin ^{2}(\alpha T)$, where $\alpha$ is a constant, and $T$ is a random variable. The $p d f$ of $\mathrm{T}$ is given by,
\[
\begin{aligned}
f(T) &=e^{-T} \text { for } T \geq 0 \\
&=0 \text { for } T<0
\end{aligned}
\]