Imagine I have for a single individual some variable $X$ with mean $\lambda$ (for example the number of cars he has). Now I take a whole population of individuals. The parameter $\lambda$ for each of them is indeed different. Assume $\lambda \sim exp (\alpha)$. Let now $X$ be the variable $Y$ for a random selected individual in such population (i.e. $X$ is the number of cars for a randomly selected individual). What is $E X$ in this case?
Thanks a lot for your help!