Suppose you have 5 temperature measurements 10, 11, 12, 13, 14 of the same object with measurement standard deviations 1, 2, 1, 3, 4, respectively. Assume the measurements are independent and the measurement errors have zero mean.

(a) Use this information to give an unbiased estimate of the true temperature with the smallest possible standard error. [Hint: weighted least sqaures.]

(I'm thinking it's probably the case (true tempeature, 10) ~(true tempeature, 14) form the linear regression? )

(b) What is the standard error of the sample mean?

(c) What is the standard error of your estimator from the first part?

Thank you!