STAT330 Lecture Notes - Lecture 4: Likelihood Function

• School: University of Waterloo
• Department: Statistics
• Course: STAT330
• Professor: Peisong Han

Document Summary

(a) since xi has c. d. f. the p. d. f. of xi is. F (x; 1, 2) = 1 (cid:18) 1 x(cid:19) 2. , x 1, 1 > 0, 2 > 0 f (x; 1, 2) = , x 1, 1 > 0, 2 > 0. Yi=1 if 0 < 1 xi; i = 1, , n and 2 > 0. 2 n 2 if 0 < 1 x(1) and 2 > 0. For each value of 2 the likelihood function is maximized over 1 by taking 1 to be as large as possible subject to 0 < 1 x(1). Therefore for xed 2 the likelihood is maximized for 1 = x(1). Since this is true for all values of. 2 the value of ( 1, 2) which maximizes l ( 1, 2) will necessarily have 1 = x(1). To nd the the value of 2 which maximizes l(cid:0)x(1), 2(cid:1) consider the function.