所屬科目：研究所、轉學考(插大)◆統計學
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 bj in terms of
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Find the moment generating function for X.
, 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
, j = O, 1. . ., k, are the associated OLS estimates.
= 0, 1, 