I know for a fact, that the theorem involves the Chi Sqaure distribution.

I am unable to solve this one. It's theorem 9.2 page 198 from P L Meyer's "Introductory Probability and Statistical Applications"

Can someone help me out with a solution?

I know how the system works, but right now, I'd be really grateful if you guys could provide a setup of the problem along side scanty hints. Our prof. hinted that this is one of sure shot questions in tomorrow's end semester exams, and none of us have been able to give it one attempt.