Let $Y$ be the number of patients (out of n) who survive for one year after an operation. Let $Z$ be the number of patients who survive for 5 years. Let $\theta=(p,q)$ and suppose that we model $Y\sim Bin(n,p)$ and $Z|Y=y \sim Bin(y,q)$.
Let $X=(Y,Z)$, find the fisher information $I(\theta,X)$
I think the first step should be to derive the distribution of $X$? Can someone help me with this step?