Question:
Let X and Y be two independent random variables having N(0, \(σ^2_1\)) and N(0, \(σ^2_2\)) distributions, respectively, where 0 < σ1 < σ2. Then which of the following statements is/are true ?
Let X and Y be two independent random variables having N(0, \(σ^2_1\)) and N(0, \(σ^2_2\)) distributions, respectively, where 0 < σ1 < σ2. Then which of the following statements is/are true ?
Updated On: Oct 1, 2024
- X + Y and X - Y are independent
- 2X + Y and X - Y are independent if \(2σ^2_1=σ^2_2\)
- X + Y and X - Y are identically distributed
- X + Y and 2X - Y are independent if \(2σ^2_1=σ^2_2\)
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The Correct Option is B, C, D
Solution and Explanation
The correct option is (B) : 2X + Y and X - Y are independent if \(2σ^2_1=σ^2_2\), (C) : X + Y and X - Y are identically distributed and (D) : X + Y and 2X - Y are independent if \(2σ^2_1=σ^2_2\).
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