Question 3 {25 marks} Suppose that you have two independent unbiased estimators of the same parameter 6' sayr HI and Hg with different variances 1:1 and tag. [a] 1What restrictions need to he placed on c1 and c2 so that it is unbiased? [b] Derive the linear combination d c131 + c232 which is the minimum variance unbiased estimator of 6'. Question 1. [25 marks} Consider the standard probit model with a latent unobserved equation 3;: = $23 | E; where E1; has a distribution function 111 and a density function :35. I} is k x 1. There are N, i.i.d., observations on the regressor x,- and a binary variable ya: {1 if fe- 3" n it Egg-:1. {a} What is the probability distribution function of EH1. conditional on 31-? [b] Derive the expected value of EH1. conditional on 31-. {c} Derive the variance of yi, conditional on m. {d} Derive the likelihood function for ,3. [e] Derive and show that the score fu_nction has zero expectation. {f} Derive the asymptotic information matrix for the MLE, ,6