Consider the linear model $\displaystyle Y_i = B_0 + B_1X_i + e_i ;\ i = 1,....,n$

where $\displaystyle e_i$ are assumed to be i.i.d. $\displaystyle N(0,stder)$ distribution, where $\displaystyle stder$ represents the standard error.

<usual notation for a normaly distributed RV would be ~N(mean,variance) >

For the LS estimators $\displaystyle b_0$ and $\displaystyle b_1$ of $\displaystyle B_0$ and $\displaystyle B_1$ show that

a) $\displaystyle cov(b_0,b_1) = -(stder)^2(\bar{X}/S_{xx}).$

b)$\displaystyle cov(\bar{Y},b_1) = 0 $. That is $\displaystyle \bar{Y}$ (the mean of $\displaystyle Y$) and $\displaystyle b_1$ are uncorrelated.

PS: I wanted to put the above in Latex by putting my math stuff between (math)....(/math) (but with square brackets) like the Latex tutorial suggested, however there seems to be something wrong with that key on my keyboard. Is there another way to do it?