why is the expected value of beta hat zero equal to beta zero?

$\displaystyle E[\hat{\beta}_0] = {\beta}_0$

in the model $\displaystyle Y_i = {\beta}_0 + B_1X_i + u_i$

$\displaystyle \hat{\beta}_0 = \bar{y} + \hat{\beta}_1\bar{x}$

if I take the expectation of both sides I get

$\displaystyle E(\hat{\beta_0}) = \mu_y + \hat{\beta}_1 \mu_x$

why is this equal to $\displaystyle \hat{\beta}_0$?

Re: why is the expected value of beta hat zero equal to beta zero?

Hey kingsolomonsgrave.

Hint: What is the distribution of the beta's? (You will need to specify the likelihood of response variable and find the MLE estimator of the beta's since MLE is equivalent to least squares)