I think that's what this question's gearing towards anyway... I'm not 100% sure, hence how I haven't a clue what to do, even after skimming through my course notes. The question goes like this...

*Suppose that $\displaystyle X_{1}$,$\displaystyle X_{2}$,...,$\displaystyle X_{n}$ are a random sample from a population with mean $\displaystyle \mu$ and variance $\displaystyle \sigma^{2}$.*

**i)** Verify that $\displaystyle X_{1}+X_{2}-2X_{3}+X_{4}$ is unbiased and has variance $\displaystyle 7\sigma^{2}$;

**ii)** Verify that $\displaystyle \frac{2X_{1}+X_{2}+X_{3}+...+X_{n}}{n+1}$ is unbiased and has variance $\displaystyle \frac{(n+3)\sigma^{2}}{(n+1)^{2}}$