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Part BCSIR NET December 2024only-one-side-of-the-interval-can-fail

Only one side of the interval can fail

Suppose that the probability density function of the random variable X is if , and 0 otherwise, where is an unknown parameter. Based on a single observation X, the confidence coefficient of the confidence interval [(2/5)X, (5/2)X] for is

  1. A.0.36
  2. B.0.55
  3. C.0.76
  4. D.0.95

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 EstimationMLE and method of moments

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