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Part CCSIR NET June 2024a-conditional-probability-free-of-the-condition

A conditional probability free of the condition

Let X and Y be jointly distributed continuous random variables with joint probability density function f(x, y) = x/y if 0 < x < y < 2, and 0 otherwise. Which of the following statements are true?

  1. A.P(X < 1/2 | Y = 1) = 1/4✓
  2. B.E(Y) = 1/4
  3. C.P(X < Y/2) = 1/4✓
  4. D.E(Y/X) = 1/4

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward.

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50 are analysed free — try those first.

Related counterexample: If X and Y are each normal and uncorrelated then they are independent

More on this topic

The chapter behind this: Joint distributions, transformations and order statistics — free to read

From Probability › Joint distributions, transformations, order statistics

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