Question

5. The sample 15. 18, 20, 19. 12, 16. 11. 7. 13, and 14 is taken from a discrete uniform distribution with a limit 21,i.e., each number is selected randomly from {1,2, .,2M}. The estimated value of I using its maximum likelihood estimator is

Answer 1

The maximum likelihood estimator (MLE) for the parameter M of a discrete uniform distribution, given the sample data, is the maximum value observed, which in this case would be 10.

Step-by-step explanation:

The question refers to the estimation of the parameter M in a discrete uniform distribution using the method of maximum likelihood estimation (MLE).

Given the sample data, we know that each value is drawn randomly from the set {1, 2, ..., 2M}, with a distribution limit of 21. Since the largest observed value in the sample is 20,

we can deduce that the parameter M must be at least 10.

Therefore, our MLE for M would be 10, as the MLE for a discrete uniform distribution is the maximum value observed in the sample.