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 X_i's are independent of the Y_i's....

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