110年 - 110 國立政治大學_碩士班招生考試_經濟學系:統計學#105666

1. (10%) Let X be a random variable with probability density function given by
   Find the moment generating function for X.

(1) (10%)

(2) (10%)

(2) (10%) Under the classical linear model assumptions, please show how to con- struct the F test statistic for the joint test H₀ : β₁ = β₂.  β₃ = 0, and write down the decision rule given the significance level a.

(3) For i =, be the standardized version of the data, where are the sample mean and sample standard deviation for y over these i observations, and are the sample mean and sample standard deviation for tj. j = 1.2. . k. Now we regress y* on 1 and xj, j = 1,2, , k, to yield the estimated model as
 where, j = O, 1. . ., k, are the associated OLS estimates.

 a. (10%) Find the OLS estimates= 0, 1, 

b. (10%) Find the t-ratio for b_j in terms of