Problem 2. Maximum Likelihood (ML) Estimation (15 points)

Suppose that we randomly select 10 students in our class and collect their weights (in pounds) as follows. 112, 120, 131, 126, 145, 158, 157, 136, 148, 176

Assume that their weights are normally distributed with unknow meanand variance. Based on the assumption, please answer the following questions.

1. Give the probability of the data set given the two parameters, i.e. the likelihoodfunction.
2. Deriveandcalculatethesolutionforbothand²usingMaximumLikelihoodEstimation.Please provide the detailed steps about getting the log-likelihood and calculating the derivative with respect to bothparameters.