Determining the random variable
Let x1, x2...xn be independent and N(o,1) distributed. Let Sn= (X^2)1+...+(X^2)n. Show that sn is a random variable x^2-distributed with d.f=n ( use Moment generating function)
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Let X1,...,Xn1 be an iid sample from N(u1,o^2) and let Y1,...,Yn2 be an iid sample from N(u2,o^2), where parameters u1,u2, and o^2 are unknown. Suppose that two samples are independent. Find a 95% confidence interval for u1-2u2.
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