Derive the likelihood function...

Suppose that we have a sample {Yi},_,, which is constructed by Y = SD, te, i = 1,...,n where {Di } is a set of dummy variables, i.e. D, = 1 with probability p and D, = 0 with probability 1 - p, and {e;} is an iid sample of Normal (#, ?) and they are independent of each other. Here note that o, p, #, and of are unknown parameters. (c) Now let's consider MLE. i. Derive the likelihood function for {Y/}. ii. Derive the likelihood function for {Yi} given {D.} iii. Obtain the MLE of the unknown parameters (except p) using the conditional likelihood in (ii). iv. Obtain the MLE of 81, which is defined in (b), and compare it with the answer in (b)