(Solution) - Complete the coverage probability calculation needed in Example 9 2 17 a If -(2025 Original AI-Free Solution)

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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) = 2?, Var(x22Y) = 8?, the mgf of X2Y is given by exp (- ? + ?/1-2t), and

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