A uniformly distributed random signal x[n] with mean m_x = 2 and variance $$\sigma _{\text{x}}^2$$ = 3, is passed through a 3-point moving-average filter having an impulse response $$\left\{ {{\text{h}}\left[ {\text{n}} \right] = \frac{1}{3},\,\frac{1}{3},\,\frac{1}{3}} \right\}.$$    What will be the mean and variance of output?

A. $${{\text{m}}_{\text{y}}} = 2,\,\sigma _{\text{y}}^2 = 1$$

B. $${{\text{m}}_{\text{y}}} = 2,\,\sigma _{\text{y}}^2 = 3$$

C. $${{\text{m}}_{\text{y}}} = 1,\,\sigma _{\text{y}}^2 = 1$$

D. $${{\text{m}}_{\text{y}}} = 3,\,\sigma _{\text{y}}^2 = 3$$

Answer: Option A