Consider a linear regression model of the form Y $=$ a $+$ b X $+$ U$,$ where U is the error and a and b are coefficients that should be estimated. Suppose that X is a binary variable $($it only takes values $0$ or $1).$ Suppose also that a and b are estimated by the OLS method. 

Prove that the OLS method will give estimates for $(1)$ E$($Y$|$X$=0)$  and E$($Y$|$X$=1)-$E$($Y$=0)$