14.2 Exercise 25

Suppose the pair $\left\{X , Y\right\}$ is independent, with $X \sim$ Poisson $\left(\mu\right)$ and $Y \sim$ Poisson $\left(\lambda\right)$. Show that X is conditionally binomial $\left(n , \mu / \left(\mu + \lambda\right)\right)$, given $X + Y = n$. That is, show that