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?
Part CCSIR NET December 2024the-sample-is-of-systems-not-components
The sample is of systems not components
Related counterexample: The MLE is unbiased
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- the prior adds one to the exponentDecember 2024
- the parameter space is open so the extremes have no mleDecember 2024
The chapter behind this: Maximum likelihood and the method of moments — free to read