Let $S$ and $T$ be two finite real random variables that are independent and defined on $(\Omega, \mathcal{A}, P)$. We assume that $T$ and $-T$ have the same distribution. Show that $E(\cos(S + T)) = E(\cos(S)) E(\cos(T))$.
Let $S$ and $T$ be two finite real random variables that are independent and defined on $(\Omega, \mathcal{A}, P)$. We assume that $T$ and $-T$ have the same distribution.
Show that $E(\cos(S + T)) = E(\cos(S)) E(\cos(T))$.