I have recieved a home assignment and the question is if $(1-|t|)e^{-|t|}$ is a characteristic function. If it is a yes, then what distribution does it correspond to?
I was wondering if that is a combination of convex characteristic functions, the Polya theorem sadly does not work. I would appreciate any ideas.
Since this is a homework problem, I will not give a full answer. The candidate characteristic function is integrable on the real line. Therefore, the candidate distribution has a density that can be computed as the inverse Fourier transform. One gets an expression for a potential density; if it qualifies, then we will also be able to determinate the distribution. If not, we will know that the aforementioned function is not a characteristic function.