Let $S$ and $T$ be two independent random variables each taking a finite number of real values. Assume that $T$ and $- T$ follow the same distribution. Show that: $$E ( \cos ( S + T ) ) = E ( \cos ( S ) ) E ( \cos ( T ) )$$
Let $S$ and $T$ be two independent random variables each taking a finite number of real values. Assume that $T$ and $- T$ follow the same distribution.
Show that:
$$E ( \cos ( S + T ) ) = E ( \cos ( S ) ) E ( \cos ( T ) )$$