Question: Let X1, X2, , Xn be a random sample from a normal N(, 2 ) distribution. (see the attached picture for complete question) Let *

Let X1, X2, , Xn be a random sample from a normal N(, 2 ) distribution. (see the attached picture for complete question)

Let * 1 , X 2 In be a random sample from a normal N ( 4 , of ) distribution Further . let 1 I1 = 2 2 ( X - * ) and T ( X 1 2 02 2 = 1 where X - - 1 Xi is the sample mean . Then : ( a ) Show that I , and I 2 are independent random variables ( b ) Identify the distributions of I , and I z

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