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 ?
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 ?
\(U=\frac{2X^2_1}{(X_2+X_3)^2}\) 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 ?
Updated On: Oct 1, 2024
- U has F1,1 distribution and V has F1,2 distribution
- U has F1,1 distribution and V has F2,1 distribution
- U and V are independent
- \(\frac{1}{2}V(1+U)\) has F2,3 distribution
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The Correct Option is A, C
Solution and Explanation
The correct option is (A) : U has F1,1 distribution and V has F1,2 distribution and (C) : U and V are independent.
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