Question

Which of the following is/ are true about  “Maximum Likelihood estimate (MLE)”?

1. MLE may not always exist
2. MLE always exists
3. If MLE exist, it (they) may not be unique
4. If MLE exist, it (they) must be unique

Answer 1

Solution: C

The MLE may not be a turning point i.e. may not be a point at which the first derivative of the likelihood (and log-likelihood) function vanishes.