For x E R", the multivariate Gaussian distribution takes the form, 1 N ( ac | M, E) = 2 3 2 (17) expl-~ (ac - M) E-1(x - M)}. case of a 2-dimensional Gaussian distribution, i . e . , x, y ~ N ( [x, y] | [/x, My] , 8 1 2 We have observed n data points {(x1, yl), (x2, 32), . .. , (In, Un) } in this distribution. (a) What is the log-likelihood of the data given (x, My, 02, (b) What is the maximum likelihood estimation for Mx, Oz (c) We say an estimator 0 of a parameter 0 is unbiased if E[0] = 0. Find out whether the maximum likelihood estimators for Mx, 2 are biased, or unbiased. Var [x] = E[x2] - E[x]2; If x and y are independent random variables, then Elxy] = E[x]Ely].)