1. Exercise 10.98: Let Y₁, Y₂, ..., Y_n be a random sample from the probability density function given by

f(y;)=(1)mym1exp(ym)wherey>0

with m denoting a known constant.

1. Find the uniformly most powerful test for testing H₀: ₀ against H_A: > ₀.

1. If the test in part (a) is to have ₀ = 100, = 0.05 and = 0.05 when _A = 400, find the appropriate sample size and critical region.