Can somebody help me please to figure out how to solve this problem:
Are the following process stationary?
$X(t) = V \cos(wt+U), t\epsilon R^1$
U and V are independent variables,
$U$ ~ $Uniform(-\pi,\pi)$, $E[V] = m_v, Var(V) = D_v$, $w \epsilon R^1$
To check stationariy I need to calculate $E, Var, Cov()$. I've tried to calculate $E[X(t)]$, but I don't understand what I can do with cosine.
$E[X(t)] = E[V*\cos(wt+U)] = E[V] * E[\cos(wt+U)] = m * $ ...
Is it possible to say that $wt+U = 0$, because $U$ has Uniform distribution? But I really not sure. Or I need to take some integral?
Thank you for your help!