I have the distribution of X with respect to parameter t vaying between 0 and 1. However, in nature, parameter t is not uniformly distributed. It has a known probability distribution. What is distribution of X given distribution of t? The product? Can you clarify, and hint at notions or concepts involved?
EDIT: in fact, problem can be formulated this way: X is a function of t,
$X: t -> X(t)$
and I would like to have an expression for P(X(t)) when I known the distribution for t.