A uniformly distributed randomsignal x[n] with mean $$m_{x} = 2$$ and variance $$\sigma_{x}^{2} = 3$$, is passed through a 3-point moving-averagefilter having an impulse response $$\left\{h[n]\right\}=\left\{\frac{1}{3},\frac{1}{3},\frac{1}{3}\right\}$$ What will be the mean andvariance of output?

A

$$m_{y}=2, \sigma_{y}^{2}=1$$

B

$$m_{y}=2, \sigma_{y}^{2}=3$$

C

$$m_{y}=1, \sigma_{y}^{2}=1$$

D

$$m_{y}=3, \sigma_{y}^{2}=3$$