This is an assignment I got for my course on Stochastic Processes:
Let us consider a random variable X distributed as a Poisson P (λ) where λ ∼ [0.5, 1].
(a) Which are the unconditional mean and variance for variable X? (DONE)
(b) Which is the probability density function of X? (Not need to solve the integral)
I managed to do the first part (a) but the second part (b) doesn't make sense to me.
How can X have a probability density function if X is a Poisson and the poisson is discrete? Am I missing something? Also, the professor says that there is no need to solve the integral, but how can there be an integral if the Poisson is discrete?
I guess the answer lies in this part:
λ ∼ [0.5, 1]
But I can't find it.