P5.7 Let U[n] be an independent and identically distributed (IID) discrete-valued random sequence with the marginal pmf at each n given by Pr [U = -4) = 0.25, Pr [U = 0] = 0.25, Pr [U =4) = 0.5, Let V[n] be another IID continuous-valued random sequence, independent of U[n], with the marginal pdf fv(v) = 1/12, -5sus7; 0, otherwise. Define a new random sequence X [n] by the equation X[n] = U[n] + V[n-1] (a) Determine the mean #y[n] and the autocorrelation Ry[m, n] of U[n]. (b) Determine the mean #v[n] and the autocorrelation Ry [m, n] of V[n]. (c) Determine the crosscorrelation Ru,v[(m, n] between U[n] and V[n]. (d) Determine the mean #x[n] of X [n]. (e) Verify that the autocorrelation of X[n] is given by Rx [m, n] = 4+ 236[m - n]. Answers: : Part (e) is sufficient to verify all other answers