Consider random processes X(t), Y (t) and Z(t), defined by X(t) = sin(0t + ), Y (t) = cos(0t + ), Z(t) = sin(0t + )

where 0 is nonrandom, U(0, 2), U(0, ) and U(0, /2) are independent.

(a) Find the mean functions of X(t), Y (t) and Z(t).

(b) Find the crosscorrelations of X(t),Y(t) and Z(t) and the average cross

powers E[X(t)Y (t)], E[X(t)Z(t)] and E[Y (t)Z(t)].

(c) Are random processes X(t), Y (t) and Z(t) orthogonal?