Question: 2(b)please only. 2. (10 marks) Let {Zt} be a sequence of independent random variables with zero mean and variance o'. For each of the following

2(b)please only.

2. (10 marks) Let {Zt} be a sequence of independent random variables with zero mean and variance o'. For each of the following parts, show that the given process { X} is weakly stationary and compute its ACF. (a) (2 marks) Xt = (-1)*Zo + (-1)ttiZ1. (b) (3 marks) Xt = Zo cos(ct) + Z1 sin(ct), where c # 0 is a constant. You may find the trigonometric identity cos(a - B) = cos a cos B + sin a sin 3 useful. (c) (3 marks) Xt = Zost + Zist-1, where { st} is seasonal with period 2. (d) (2 marks) Xt = ZZt-1 ... Zt-k, where k is a positive integer

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