Let X1, X2, ..., X10 be a random sample of size 10 from a Poisson distribution with parameter θ. Let L(θ) be the joint pdf of X1, X2, ..., X10. The problem is to test H0 : θ = 1/2 vs H1 : θ = 1. (a) Show that L(1/2)/L(1) ≤ k is equivalent to Y = P10 i=1 Xi ≥ c. (b) In order to make α = 0.05, show that H0 is rejected if Y > 9 and, if Y = 9, reject H0 with probability 1/2 (using some auxiliary random experiment).