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 = .4; at level of significance α = .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.]