1. We call a dummy variable, any random variable d that can only take values 0 or 1. In this exercise you will be asked to prove some results about regressions with dummy variables. Consider the following simple regression model: i=1,..., n, where di is a realization of the dummy variable d, that can either be 0 or 1. (a) When di 0, you have the simple regression model: Yi = Bo + ui. = (b) When di Show that Bo= E(yildi = 0). Yi Bo + Bidi+Ui, = = 1, you have the simple regression model: Yi Bo + B + U. (1) Show that Bo + = E(yildi = 1). (c) Use the results in (a) and (b), to provide a formula for Bo and B. (d) Construct an estimator for Bo and B, using their definition as conditional expectations.