more Estimation....

[Michelle]

This question asks for relative efficiency..
X and Y are random sample from a population with mean mu and variance sigma squared. (assume that X and Y are indeoendently distributed).
Consider the following two point estimators of the population mean.
1)0.31X+ 0.69Y
2)0.37X+ 0.63Y

(both estimators should be unbiased.

Question is find the relative effiency:
THe formula is
Var (theta2)
-----------
Var (theta 1)

I would appreciate yourhelp.

[quark]

Michelle,

Sincce X and Y are independent, this is quite straightforward. Just apply the formula Var[aX+bY] = a^2*Var(X) + b^2*Var(Y) to 1) and 2) and compute the ratio to find the relative effiency.