If X∼Poisson(λ)X \sim Poisson(\lambda)X∼Poisson(λ) and Y∼Poisson(μ)Y \sim Poisson(\mu)Y∼Poisson(μ) are independent, what is the conditional distribution of XXX given X+Y=nX+Y = nX+Y=n?
Poisson (λ+μ)(\lambda + \mu)(λ+μ)
Binomial (n,λλ+μ)(n, \frac{\lambda}{\lambda+\mu})(n,λ+μλ)
Normal (λ,λ)(\lambda, \lambda)(λ,λ)
Geometric (p=μλ+μ)(p = \frac{\mu}{\lambda+\mu})(p=λ+μμ)