18.05 Lecture Notes - Lecture 5: Mit Opencourseware
Document Summary
Problem 1. (10 pts. ) (a) we know that yi axi b = i n(0, 2). Therefore yi = i + axi + b n(axi + b, 2). 1 f (yi | a, b, xi, ) = . 2 2 (b) (i) the y values are 8, 2, 1. The likelihood function is a product of the densities found in part (a) f (8, 3, 2 | a, b, ) = ((8 a b)2+(2 3a b)2+(1 5a b)2)/2 2 e ln(f (8, 3, 2 | a, b, )) = 3 ln( ) ln(2 ) . 2 (8 a b)2 + (2 3a b)2 + (1 5a b)2. 2 2 (ii) we just copy our answer in part (i) replacing the explicit values of xi and yi by their symbols f (y1, . J=1(yj axj b)2/2 2 e n ln(f (8, 3, 2 | a, b, )) = n ln( ) n. 2 ln(2 ) (yj axj b)2/2 2 n n j=1.
