STAT371 Lecture Notes - Lecture 18: Central Limit Theorem, Likelihood Function, Random Variable

• School: University of Waterloo
• Department: Statistics
• Course: STAT371
• Professor: Hany Fahmy

Document Summary

Rationale: ml: find -hatml that maximizes the likelihood that f is coming from your sample data. Ut is independent, identically distributed as normal distribution (iidn). {-1/2 ((ut - 0)/ )} #1, jointly classified of n independent random variables is the product of the marginals: f (u | =0, ) = [1/( (2 ) )] exp. F (u | =0, ) = [1/( (2 ) )] exp. {-1/(2 ) u u} #3: yt is a function of a normally distributed random variable ut, t. Yt ~ iidn ( + x t + + kxkt, ), t: by change of variables, f (yt) = f (ut) F (yt | , , , k, ) = 1/( (2 ) ) exp. - kxkt) } #4, = [ , ], Rational ml, l is the likelihood function: -hatml = average max l( | y, first, linearize l: