辅导案例-ETC3400-Assignment 3
ETC3400-BEX3400-ETC5340: PRINCIPLES OF ECONOMETRICS Solutions to Assignment 3, Semester 2, 2020 1. Suppose that the discrete random variable Y has a one parameter probability density function which is given by f (yj) = (1 )y ; y = 0; 1; 2; :::; 0 < < 1: The mean and variance 2 of this distribution are equal to 1 and (1 )2 respectively. Suppose that we have a sample of n i.i.d observations on this variable, fy1; y2; :::; yng. (a) Show that the maximum likelihood estimator of is ^MLE = y y + 1 ; where y is the sample mean of fy1; y2; :::; yng : L(; y1; y2; :::; yn) = i=nY i=1 (1 )yi = (1 )nyi ; =) l(; y1; y2; :::; yn) = n log(1 ) + i=nX i=1 yi log ; ) @l @ =