Question:

Let \( X \) and \( Y \) be continuous random variables having the joint probability density function
\[ f(x, y) = \begin{cases} e^{-x}, & \text{if } 0 \leq y < x < \infty \\0, & \text{otherwise}\end{cases} \]
Then which of the following statements is/are correct?

Updated On: Oct 1, 2024
  • \( P(Y^2 = 3X) = 0 \)
  • \( P(X > 2Y) = \frac{1}{2} \)
  • \( P(X - Y \geq 1) = e^{-1} \)
  • \( P(X > \ln 2 \mid Y > \ln 3) = 0 \)
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The Correct Option is A, B, C

Solution and Explanation

The correct option is (A): \( P(Y^2 = 3X) = 0 \),(B):,\( P(X > 2Y) = \frac{1}{2} \),(C): \( P(X - Y \geq 1) = e^{-1} \)
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