Construct the t-test ...and find its asymptotic distribution

1. Consider the linear regression model yi = Tip + ei er; ~ N (0, cail), where c is an unknown positive constant. (a) Note that we assume that e, given a; has a normal distribution. Util- ising this information, we estimate S using the maximum likelihood method. Show the consistency of the MLE of / and derive its asymp- totic distribution. (b) Construct the t-test statistic for the null hypothesis of S = 1 and find its asymptotic distribution