Let X be distributed as N(,2). The unknown parameters are and 2. (a) Find the log-likelihood

Let X be distributed as N(¹,¾2). The unknown parameters are ¹ and ¾2.

(a) Find the log-likelihood function `n(¹,¾2).

(b) Take the first-order condition with respect to ¹ and show that the solution for b¹ does not depend on ¾2.

(c) Define the concentrated log-likelihood function `n(b¹,¾2). Take the first-order condition for ¾2 and find the MLE b¾

2 for ¾2.