Consider a dataset with three observations (Y1, Y2, Y3) and (X1, X2, X3) where the Y's are binary outcomes. Write the likelihood functions of logit model where Z = beta 0 + beta 1 X + beta 2 X2 Write the likelihood for the probit model as well. Write the expression for the change in the probability that Pr(Y = 1|X) for a unit change in X under the linear probability model Y = beta 0 + beta 1 X + beta 2 X2 Write the expression for the change in the probability that Pr(Y = 1|X) for a unit change in X under the logit model for Z. Write the log-likelihood for the logit model. Write first order conditions of the log-likelihood of the MLE logit estimator for (beta 0, beta 1, beta 2). This question deals with the dataset of American Express credit card applicants AmEx.dta. For each part, you will need to report results for the linear probability model, logit, and probit models. The best way to organize your results is in the form of a table. Report the log-likelihood and pseudo R2 for the nonlinear models and the R2 and adjusted R2 for the linear model