申論題

5.(15%) Let X and Y be two independent random variables that follow a Poisson distribution with rate parameter θ and λ, respectively, i.e., X ~ Poisson(θ) and Y ~ Poisson(λ), Show that the distribution of X/(X+Y) is binomial with success probabilityθ/(θ+λ).
Note: the probability density function of a Poisson distribution with rate parameter y is