# how to find the efficient estimator

I know in general if we have two unbiased estimator $$T_1$$ and $$T_2.$$ then $$T_1$$ is a more efficient estimator of $$T_2$$ if $$Var(T_1). However in this problem, it asked me to what that an estimator is most efficient:

Problem: Let there be two independent random samples containing $$n_1$$ and $$n_2$$ values made out of a random variable $$X$$ with $$\mu$$ and $$\sigma ^2$$.

b) Show that the most efficient estimator $$T_1$$ can be given in the form $$\frac{n_1 \bar{X_1}+n_2 \bar{X_2}}{n_1+n_2}$$.

I can do part a), but I am not sure about part b), I do not know what I have to show. I mean if they give me two estimators than I could try to compute variance, but it only gives me one estimator and asks me to show it is the "most efficient". Is there a general way to do problems like this? I would appreciate the help.