The question below is already answered in the explanation. Please walk me through each step on what is happening and why. Explain thoroughly and give a clear explanation of the terms and steps.

Explanation . The maximum likelihood can be obtained by, n L(B, 02) = II 1 (yi - Baci)2 exp i=1 V2102 202 . Solve the above equation. n L(B, 02) = II 1 (yi - Baci) 2 exp i=1 V27102 202 = exp Eil(yi - Bxi)2 2702 202 . Maximising L will leads to, In L(B, 62) = 2 In(2702) + Li-1(yi - Bxi)2 202 . The above requires choosing B to minimise H (B) = Et-, (yi - Bai)2. H'(B) = 2 (yi - Bxi) i=1 = 0 B = Liliyi . The B = Li Liliyi which is a point of minimum since H" (B) = 2 ET-1 x? > 0. aln L(B, 02) n Ei=1(yi - Bai)2 a(02 ) 202 2(02) 2 = 0 62 1 = n E(yi - Back)? i=16.5: A SIMPLE REGRESSION PROBLEM Problem 1. In some situations where the regression model is useful, it is known that the mean of Y when X = 0 is equal to O, that is, Y; = [33;- +61: where 61- for 2' = 1, 2, . . . ,n are independent and JV(O, 0'2). (1) Obtain the maximum likelihood estimators, E and 92, of 5 and 02 under this model