Say we have the function f = (1/(sqrt(2*pi))) * exp((-1/2) * min(1,t^2)). If I understand it correctly, the min() function means that this function is constant for any t greater 1 and any t smaller than -1. We could also say, it is uniform between 1 and infinity, as well as uniform between minus infinity and minus one. It has a bell shaped form in between -1 and 1. I know that a PDF in order to be valid has to integrate to 1. Here, I would argue that it isn't a valid PDF, because the integral never converges. Even if I multiplied by any factor, I could never decrease the height in a way that would allow integration to 1. Is this correct