Question

Let 𝑋 and 𝑌 be i.i.d. random variables each having the 𝑁(0, 1) distribution. Let 𝑈=$\frac{𝑋}{𝑌}$ and 𝑍=|𝑈|. Then, which of the following statements is/are TRUE?

• A. 𝑈 has a Cauchy distribution
• B. 𝐸(𝑍𝑝)<∞, for some 𝑝 ≥ 1
• C. 𝐸(𝑒𝑡𝑍) does not exist for all 𝑡∈(−∞, 0)
• D. 𝑍 2~𝐹1,1

Answer 1

Answer: (A), (D)

𝑈 has a Cauchy distribution

Answer 2

The correct options are: A and D