I have to find the random variable $X$ s.t. $\psi(t)=\cos(t)$ is its characteristic function.
I'm trying to use the inversion formula $f(x)=\int_{-\infty}^{+\infty} e^{-itx}\psi(t)dt$ but it seems to get me nowhere.
Is there some kind of trick on this? I also tried to find the distribution making a sequence $\psi_n \to \psi$ from the Taylor expansion of $\cos(t)$ but also nothing.