# Ols estimator with the errors following a bernoulli distribution

I am having trouble understanding how i should approach the following problem: Given 𝑦𝑖 = 𝛼 + 𝛽𝑥𝑖 + 𝜀𝑖 𝑖 = 1, … , N with 𝜀𝑖 𝑖 = 1,2 … , N being a succession of IID Bernoulli variables with Pr({𝜀𝑖 = 1}) = 1 , Pr({𝜀𝑖 = 0}) = 1 − P 0 < 𝑝 < 1 (p is a known parameter). Find the OLS estimators for 𝛼̂ e $$\widehat{𝛽}$$.

From this thread, it would appear that the given residuals are missing the mean=0 and costant variance requirements for the ols to be BLUE.

What would the estimated $$\widehat{Y}$$ function look like? Would the 𝜀𝑖 term disappear as usual?