No need for long explanation or proof. Please do show your working though. I"m looking to confirm my answers. Thank you!!!

1. Use words, and without using symbols, describe the differences between strictly stationary and weakly stationary, and why is stationarity important? 2. Let Zt = U sin(2nt) + V cos(2xt), where U and V are independent random variables, each with mean 0 and variance 1. (a) Is Zt strictly stationary? (b) Is Z, weakly stationary? 3. Suppose wt follows i.i.d Normal distribution N(0,1). For each of the following, state if it is a sta- tionary process. If so, give the mean and autocovariance functions. (a) Zt = wt - Wt-3 (b) Zt = we + t 4. Suppose Yt = 5+ 4t+ Zt, where { Z} is a zero mean stationary series with autocovariance function Yk . (a) Find the mean function for Yt. (b) Find the autocovariance function for Y. (c) Is Yt weakly stationary? (Why or why not?)