QUESTION

I had a 10cm pole which broke in half. The two peices were measured and this resulted in values of and respectively.

If the true 'correct' length of the first peice is given as and the standard deviation of the two measurements is

1) Then find the least-square estimate of

2) Find the standard error of the estimate in (1) in terms of

My Answer so Far

By Least-Squares Definition we minimize distance

Take derivative and set to zero? This is where I am unsure? *Thanks*

If I do this I get

This solves to

Is this somewhere close?

2)

Now Im also unsure of this variance property.. but I solve to get

Is it right that the variance of the 10 is zero.. so it just leaves the equation?

Thanks very much for any help advice