Consider the linear model

where are assumed to be i.i.d. distribution, where represents the standard error.

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

For the LS estimators and of and show that

a)

b) . That is (the mean of ) and 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?