I have the next problem.Let $X$ be a random variable with Bernoulli's distribution $Ber(p)$. For every $t\geq0$ define the variable
$X_{t}=\begin{cases} \cos (\pi t), & \text{if $X$ = 0} \\ \sin(\pi t), & \text{if $X$ = 1} \end{cases}$
I have to compute the distribution of $X_{t}$ and $E(X_{t})$ but I don't know how to do this, because I remember when I have the random variable with this distribution but I don't know how to apply in this case.