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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(9,θ),0.7<θ<1(9, \theta), 0.7 < \theta < 1, and Y ~ Poisson(λ),λ>0(\lambda), \lambda > 0. 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)✓ Correct

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, and why this one tests boundary and endpoint.

See pricing

50 are analysed free — try those first.

The trap it tests

Boundary and endpoint

The statement turns at the edge of the interval, the domain, or the parameter range.

Drill statements like this

Related counterexample: The maximum of independent exponentials is exponential

More on this topic

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

From Probability › Standard discrete and continuous distributions

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