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).

The height of a birch tree, f(x), in inches, after x months is shown in the graph below. how much does the birch tree grow per month, and what will be the height of the birch tree after 10 months? a. the birch tree grows 1 inch per month. the height of the birch tree will be 16 inches after 10 months. b. the birch tree grows 2 inches per month. the height of the birch tree will be 26 inches after 10 months. c. the birch tree grows 3 inches per month. the height of the birch tree will be 36 inches after 10 months. d. the birch tree grows 2 inches per month. the height of the birch tree will be 24 inches after 10 months.