This is about log-likelihood function question. I have no idea for this

Assume that X is a random variable with density corresponding to an equal mixture of two Gaussians, with unknown means p1,,u2 and unknown variances 01, 0'21 m) = 0.5mm, a?) + 0.5mm, 03). (1) Assume you are given a dataset of n iid samples from this distribution: D = {:01 H121. Your goal is to estimate mung, 01 and 02. (a) [10 MARKS] Write down the negative loglikelihood for this problem, for the given dataset D = {ch L1. Simplify as far as you can, by explicitly writing the densities for a Gaussian. Hint: You will not be able to simplify very far, and you will be stuck with a few exponentials that the logs cannot cancel. (b) [10 MARKS] Derive update rules to estimate #1,,112, 01, and 02. More specically, derive the gradient descent update rule7 for the negative log likelihood you provided above