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Part BCSIR NET December 2025compare-all-four-likelihoods-a-tie-among-distractors-is-not-the-max

Compare all four likelihoods a tie among distractors is not the max

Let X be a Binomial(n, p) random variable, where n ∈ {5, 6} and p ∈ {1/4, 3/4}. If X = 3 is observed, then the maximum likelihood estimate of (n, p) is

  1. A.(5, 1/4)
  2. B.(5, 3/4)✓
  3. C.(6, 3/4)
  4. D.(6, 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: The MLE is unbiased

More on this topic

The chapter behind this: Maximum likelihood and the method of moments — free to read

From Estimation › MLE and method of moments

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