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Prove that the expression given below follows a t-distribution with 2 degrees of freedom. Let X1 and X2 be random samples of size 2 from

Prove that the expression given below follows a t-distribution with 2 degrees of freedom.

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Let X1 and X2 be random samples of size 2 from N(0,1), and Y1 and Y2 be random samples of size 2 from N(1,1). Suppose further that the Xi's are independent of the Yi's. Prove and explain that X1+X2 follows a t- (YzY1)2+(X2 'Xz 'J 2 distribution with 2 degrees of freedom

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