Question

Maximum Likelihood Estimation

Height is normally distributed in the male population with expected value 70 inches and variance 6 inches. In the female population, height is also normally distributed with expected value 64 inches and variance 6 inches. Which of the following samples is more likely to have been drawn from the male population?

(i) one person with a height of 70 inches.

(ii) three people with heights 68, 68, and 71 inches.

Answer 1

As male population has expected value 70 hence it male population is more concentrated near to 70 and similarly female population is more concentrated at 64.

i. As here only one person is with height of 70 inches which is far away from 64 hence this sample is more likely from male population.

ii. Here also all three people with heights 68,68 and 71 are near to 70 and far away from 64. Hence, this sample is also more likely to have been drawn from male population.

Thank you.