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Part CCSIR NET December 2023

Random variables, distributions, moments, MGF

Let X be a discrete random variable with support S = {−1, 0, 1} and P(X = 0) = 1/3. Then which of the following statements are true?

  1. A.E(X) ≤ 2/3✓ Correct
  2. B.E(X2)=2/3E(X^{2}) = 2/3✓ Correct
  3. C.E(|X|) = 2/3✓ Correct
  4. D.Var(X) > 2/3

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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Related counterexample: Uncorrelated ⇒ independent

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The chapter behind this: Random variables, moments and generating functions — free to read

From Probability › Random variables, distributions, moments, MGF

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