Derive the likelihood function..

Suppose that we have a sample {K}?=1, which is constructed by Y; = 6D; +65, i=1,...,n where {13,-} is a set of dummy variables, i.e. D.- = 1 with probability p and D; = U with probability 1 p, and {8;} is an iid sample of Normal (34,02) and the}f are independent of each other. Here note that 5, p, ,u, and 0'2 are unknown parameters. Now let's consider MLE. i. Derive the likelihood function for {E}. ii. Derive the likelihood function for {Ye} given {1);}. iii. Obtain the MLE of the unknown parameters (except p) using the conditional likelihood in (ii). iv. Obtain the MLE of {31, which is dened in (b), and compare it with the answer in (b)