Complete the coverage probability calculation needed in Example 9.2.17.
a. If X22Y is a chi squared random variable with Y ~ Poisson(A), show that E(x22y) = 2λ, Var(x22Y) = 8λ, the mgf of X2Y is given by exp (- λ + λ/1-2t), and

as λ †’ ˆž. (Use moment generating functions.)
b. Now evaluate (9.2.22) as λ †’ ˆž by first standardizing X22Y- Show that the standardized upper limit goes to - ˆž as λ †’ ˆž, and hence the coverage probability goes to 0.

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