Let U = (Un : n Z) consist of independent random variables, each uniformly distributed on the interval [0, 1]. and let X

= (Xk : k Z} be defined by Xk = max{Uk1, Uk}.

(a) Sketch a typical sample path of the process X.

(b) Is X stationary? (c) Is X Markov? (d) Describe the first order distributions of X.

(e) Describe the second order distributions of X.