If $x[n]$ is a discrete random sequence with uniform distribution having mean $\mu = 2$ and variance $\sigma^2 = 3$, if passed through a moving average filter to get an output of
$$\frac{x[n] + x[n-1] + x[n-2]}{3}$$
what would be the the variance of the new signal?
I am getting 2 answers like 1 and 3. Which is correct?