Suppose thatX_i , fori= 1, 2, ..., n, are random variables such that E(X_i) =for alli= 1, 2, ..., n. Herea_i , fori= 1, 2, ..., n, are constants. Under what condition will

n

E( a_i X_{i ) =} be true?

i=1

Explain how you would justify the use of eachof the following techniques to estimate a parameter, noting any possible limitations:

method of moments estimation

least squares estimation

maximum likelihood estimation.