A random variable (X) has distribution function [F_{alpha}(x)=e^{-alpha / x} ; alpha>0, x>0] (Frecht distribution). What distribution type arises when mixing this distribution with regard

A random variable \(X\) has distribution function

\[F_{\alpha}(x)=e^{-\alpha / x} ; \alpha>0, x>0\]

(Frechét distribution).

What distribution type arises when mixing this distribution with regard to the exponential structure distribution density \(f(\alpha)=\lambda e^{\lambda \alpha} ; \lambda>0, \alpha>0\) ?