Question:

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

Updated On: Oct 1, 2024
  • π‘ˆ has a Cauchy distribution
  • 𝐸(𝑍𝑝)<∞, for some 𝑝 β‰₯ 1
  • 𝐸(𝑒𝑑𝑍) does not exist for all π‘‘βˆˆ(βˆ’βˆž, 0)
  • 𝑍 2~𝐹1,1
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The Correct Option is A, D

Solution and Explanation

The correct options are: A and D
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