Originally Posted by

**chella182** *Suppose that $\displaystyle X_{1}, X_{2},...,X_{n}$ are independently and identically distributed variables in a random sample drawn from a population with mean $\displaystyle \mu=20$ and variance $\displaystyle \sigma^{2}=9$.*

**a) **Determine the mean and variance of $\displaystyle Y=\frac{3X_{1}+2X_{2}+X_{3}+...+X_{n}}{n+3}$.

**b) **Construct your own unbiased estimator for the population mean, and calculate its variance.

I'm not entirely sure what I'm doing for **a)** and I don't know what to do for **b)** at all. Can anyone help?