Question

Let X1, X2 and X3 be three independent and identically distributed random variables having N(0, 1) distribution. If
$U=\frac{2X^2_1}{(X_2+X_3)^2}$ and $V=\frac{2(X_2-X_3)^2}{2X^2_1+(X_2+X_3)^2},$
then which of the following statements is/are true ?

• A. U has F1,1 distribution and V has F1,2 distribution
• B. U has F1,1 distribution and V has F2,1 distribution
• C. U and V are independent
• D. $\frac{1}{2}V(1+U)$ has F2,3 distribution

Answer 1

Answer: (A), (C)

U has F1,1 distribution and V has F1,2 distribution

Answer 2

The correct option is (A) : U has F1,1 distribution and V has F1,2 distribution and (C) : U and V are independent.