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Part CCSIR NET December 2024the-sample-is-of-systems-not-components

The sample is of systems not components

Consider a manufacturing unit producing three-component series systems, where component's lifetimes are independent and identically distributed random variables with hazard function if x > 0, and 0 otherwise. Here, is an unknown parameter. Let be a random sample of size 3 on lifetimes of systems produced by the manufacturing unit. Let . If ̂ is the maximum likelihood estimate of based on the realization of the random sample, then which of the following statements are true?

  1. A.̂ ∈ (0.0, 0.2)
  2. B.̂ ∈ (0.1, 0.3)
  3. C.̂ ∈ (0.2, 0.4)
  4. D.̂ ∈ (0.3, 0.5)

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.

See pricing

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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