Question

Let 𝑋₁, 𝑋₂, 𝑋₃ be 𝑖. 𝑖. 𝑑. random variables, each having the 𝑁(0, 1) distribution. Then, which of the following statements is/are TRUE?

• A. \(\frac{\sqrt2(X_1-X_2)}{\sqrt{(X_1+X_2)^2+2X^2_3}} ∼𝑡_1\)
• B. \(\frac{(X_1-X_2)^2}{\sqrt{(X_1+X_2)^2+2X^2_3}} ∼F_{1,2}\)
• C. \(E(\frac{X_1}{X^2_2+X^2_3})=0\)
• D. 𝑃(𝑋₁ < 𝑋₂ + 𝑋₃ ) =\(\frac{1}{3}\)

Answer 1

The Correct Option is C

The correct option is (C): \(E(\frac{X_1}{X^2_2+X^2_3})=0\)