Let f_tgt_1 be an i.i.d. sequence of random variables N(_2) and _ real parameter. Consider the sequence fxtgt_1 de_ned by: x1 = _1; xt = _xt􀀀1 + _t (t _ 2): In what follows, consider _ = 0. (a)...

Let f_tgt_1 be an i.i.d. sequence of random variables N(_2) and _

real parameter. Consider the sequence fxtgt_1 de_ned by:

x1 = _1; xt = _xt􀀀1 + _t (t _ 2):

In what follows, consider _ = 0.

(a) Calculate V (xt)

(b) Calculate Cov(xt; xt􀀀k), 0 _ k _ t

(c) What is the distribution of xt?

(d) For what values of _, (xt) converges in distribution?

(e) What is the distribution of (x1; x2 xn)? Calculate its probability density.

(f) Is this process stationary?