Is $\gamma(t)=\cos^2(t)$ a characteristic function?

Question

Is $\gamma(t)=\cos^2(t)$ a characteristic function?

I don't know how can I show that $\gamma(t)=\cos^2(t)$ is a positive function.

Answer 1

Use and show the following facts:

• if $X$ and $Y$ are two independent random variables, the characteristic function of $X+Y$ is the product of the characteristic functions of $X$ with that of $Y$;
• the function $t\mapsto \cos t$ is a characteristic function.