Suppose \(Y_{t}\) follows a random walk, \(Y_{t}=Y_{t-1}+u_{t}\), for \(t=1, \ldots, T\), where \(Y_{0}=0\) and \(u_{t}\) is i.i.d. with mean 0 and variance \(\sigma_{u}^{2}\).

a. Compute the mean and variance of \(Y_{t}\).

b. Compute the covariance between \(Y_{t}\) and \(Y_{t-\mathrm{k}}\).

c. Use the results in (a) and (b) to show that \(Y_{t}\) is nonstationary.