In class, we introduce two different concepts to study the relationship between X and Y. The first object was the Conditional Expectation Function (CEF), and the second object was the univariate linear regression model (LRM). Although the CEF is not always linear, when it is linear, then the LRM is the CEF. One special case where the CEF is linear is when X takes one of two values as follows: Consider E[Y|X] where X is a dummy variable that equals one with probability p and is zero otherwise. Prove that the CEF and the regression of Y on X are the same in this case. Do this by showing that for Bernoulli X: a = [[Y] - BE[X] = [[Y|X = 0] B = Cov(X, Y)/V(X) = ([[Y|X = 1] - E[Y|X = 0])