A simple way to reduce noise is to perform what is called a moving average filter on a signal. Mathematically, the moving average filter is a discrete-time random process described by Y _n = 1/L sigma^n_k = n - L + 1 X_k
where X_k are the original input random process needing noise reduction. Assume that the process X_k is IID and has mean 2 and variance 3.
a. Find the mean and variance of Y_n for L = 12.
b. Based on the Central Limit Theorem, write an expression for the PDF of Y_n.
c. How large should L be to have the variance Y_n be less than 0.1?
d. For the value of L computed in part (c), what is Pr [|Y_n - E{Y_n}|] > 0.1?