Q3 (8 pts): Maximum Likelihood Estimation The probability density function of a Gaussian distribution with parameters, mean / and variance o is given by: 1 f (2; 1, 02) (a - M) 2 V2702 exp 202 Consider a set {X1, X2, ....., XN} of N independent and identically distributed Gaussian random variables, with parameters /, 0. 1. (4 pts) Write the expression for the negative log-likelihood NLL(X1, . . ., XN) = - log P(X1, X2, . ...., XN; H, 2) using the Gaussian density function given above.2. (4 pts) Compute the gradient of the negative log-likelihood with respect to / and o (it should be a function of X1, X2, ....., XN). Include all derivation steps for full credits. Hint: There are two gradients that need to be computed: NLL(X1, ..., XN) and NLL(X1, ..., XN)