Given X1,...,X7, a random sample from a population of mean mu and variance sigma^2. Prove that the following estimators are unbiased:
estimator 1 = (X1+...X7)/7 = mean = unbiased by definition,
my problem is with the second one:
estimator 2 = (2X1 - X6 + X4) / 2
Then they ask which estimator is the best, so that I kinda know, it will be the estimator with the lower variance but I can't solve for the variance because I have no numbers.
And then they ask for efficiency...needless to tell that I don't know that 1 either.
Much appreciate it guys!!
Thanks a lot. Show me the following if you don't mind :P
I wana calculate relative efficiency of the 2, they say it's:
MSE(estimator) = E( estimator - teta)^2
and relative efficiency is: MSE(estimator1)/MSE(estimator2)
I got trouble calculating the MSE of each estimator, those symbols mix me up badly lol :P