Hi guys, can someone help me in this one?
I need to prove that $$P(X = k) = \frac{\theta}{(1 + \theta)^{k+1}}$$, where $$X ~ Poisson(\lambda = y) and Y ~ Exponential(\theta) $$
I know that $$P(X = k) = \frac{e^{-y} y^k}{k!} $$ and $$ P(Y = y) = \theta \cdot e^{-\theta y} $$
I don´t understood how to relate these two formulas.