Please show a step by step solution for the following and

possibly R code for part B.

1. Define the moving average where wt is the standard normal white noise, 500 x, = 2w,+,-/i,r= 1, , 1000. i=1 a. Calculate the variance of x,. b. Simulate and plot x1 , ,xlooo. c. Calculate how many values of x, that lie two standard deviations from the mean. Does the number look reasonable to you