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Part BCSIR NET December 2024the-stated-range-of-theta-decides-it

The stated range of theta decides it

Suppose that X ~ binomial, and Y ~ Poisson. If 3E(Y) = E(X), then which of the following is true?

  1. A.Var(X) > 3Var(Y)
  2. B.2Var(Y) < Var(X) < 3Var(Y)
  3. C.Var(Y) < Var(X) < 2Var(Y)
  4. D.Var(X) < Var(Y)

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: The maximum of independent exponentials is exponential

More on this topic

The chapter behind this: The standard distributions — free to read

From ProbabilityStandard discrete and continuous distributions

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