give explanation

2. We consider an altered regression problem for random variables X and Y. Let 2:1, . . . ,th be the values observed from a random sample of X. We assume that the conditional expected value of Y depends linearly on the value of X , and that we know that the slope of the line is double the yinteroept; in other words, we assume Yi=+2w+n where [3 is unknown, 51, . . . ,5\" are independent and identically distributed N (0, 0'2) with un- known 02. (a) (10 points) Find the maximum likelihood estimators for B and 0'2. Show all work that justies your answer. (b) (4 points) Suppose you take three samples and observe (x1, y1) = (1, 4), (202, y2) = (0, 1), and (23, 93) = (3, 6). Compute the point estimate for / using the maximum likelihood estimator from part (a).(c) (4 points) What are the residuals for this model? What do the residuals measure? Hint. The maximum likelihood estimator for a2 is the average of the squares of the residuals