please use R programming thanks!

5. Gaussian White Noise and its square. Let {Zt} be a Gaussian white noise, that is, a sequence of i.i.d. normal r.v.s each with mean zero and variance 1. Let Yt = Z?. (a) Using R generate 350 observations of the Gaussian white noise Z. Plot the series and its acf. (b) Using R, plot 350 observations of the series Y = Z?. Plot its acf. (c) Analyze graphs from (a) and (b). - Can you see a difference between the plots of graphs of time series Z and Y? From the graphs, would you conclude that both series are stationary (or not)? - Is there a noticeable difference in the plots of acf functions pz and py? Would you describe Y as a non-Gaussian white noise sequence based on your plots? Provide full analysis of your conclusions. (d) Calculate the second-order moments of Y: My (t) = E(Yt), of (t) = Var(Yt), and py (t, t + h) = Cor(Yt, Ytth). Do your calculations support your observations in (c)? Hints: (i) Slides 65 and 68 of week 1 have R commands to generate MA(1) time series. White Noise is a MA(1) process with coefficient 01 = 0. Here is a more direct code to generate WN {Zt} ~ N(0, 1) : Z