I have a question about how to find the pdf of a random variable $Z$ which is a sum and product of continuous AND discrete random variables.
More specifically, I know that $X$ is Bernoulli($p$) and I have an expression for the continuous pdf of $Y$, as \begin{align*} f_y(t) = \left\{ \begin{array}{ll} ... \qquad & \text{for } t \in [a,b] \\ 0 & \text{otherwise} \end{array} \right. \end{align*} How would I find the pdf of $Z=XY$ ? If anyone could help me/has a good reference for this kind of question I would really appreciate.
Thank you very much