Let X and Y be independently distributed with Poisson distributions P() and P(). Find the power of

Let X and Y be independently distributed with Poisson distributions P(λ) and P(μ). Find the power of the UMP unbiased test of H : μ ≤ λ, against the alternatives λ = .1, μ = .2; λ = 1, μ = 2; λ = 10, μ = 20; λ = .1, μ = 0.4; at level of significance α = 0.1.

[Since T = X + Y has the Poisson distribution P(λ + μ), the power is

β = ∞

t=0

β(t)

(λ + μ)t t! e−(λ+μ)

, where β(t) is the power of the conditional test given t against the alternative in question.]