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: yi = β0 + β1di + ui , i = 1, . . , n, (1) where di is a realization of the dummy variable d, that can either be 0 or 1. (a) show that β0 = e(yi |di = 0). (b) show that β0 + β1 = e(yi |di = 1). (c) use the results in (a) and (b), to provide a formula for β0 and β1. (d) construct an estimator for β0 and β1, using their definition as conditional expectations.