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 resualts about regressions with dummy variables. Consider the following simple regression model: where di is a realization of the dummy variable d, that can either be 0 or 1. (a) When d0, you have the simple regression model: Show that oE(ldi0) (b) When d 1, you have the simple regression model: Show that A) + ,-E(Vild, = 1). (c) Use the results in (a) and (b), to provide a formula for Bo and B (d) Construct an estimator for Bo and B1, using their definition as conditional ex- pectations