What is the distribution of a exponential distribution, whose parameter is drawn form the gamma distribution
$$ X \sim \operatorname{Gamma}(\alpha,\beta)$$
$$ Y \sim \operatorname{Exp}(X)$$
how is $Y$ distributed?
EDIT Since there are different ways of expressing the gamma distribution I will state the distributions that lead to heropup's correct answer.
the pdf of the gamma distributed variable $X$ is given by
$$f_X(x) = \frac {\beta^{\alpha}}{\Gamma (\alpha)} x^{\alpha -1} e^{-\beta x}$$
and the pdf of the compound exponenetial variable $Y$ is given by
$$f_{Y\mid X}(y\mid x) = Xe^{-Xy}$$