evaluate the expectation:
So I have 3 independent populations with μ1, μ2, and μ3.
It is given to calculate their average we use L= (μ1+μ2) - μ3
We have random samples for each population with respective sample mean Y1, Y2, and Y3.
Then we get the estimator l= (Y1 + Y2) - Y3
. _
So the Question is: Is l an unbiased estimator for L?
I know in order to be an UE the expected value of the estimator has to be equal to the actual value, but how do we show this?
wow that is very simple!
One more question, if each population has the same population standard deviation σ=5 and each sample is of size n=10.
Compute the variance of the estimator l. That is, compute σ^2{l}.
From class I learnt that σ^2{l}=σ^2/n, but how do I use that to solve it?