Homework Answers
a) 
Autocovariance is 
![EIA2e tt2) cos(t) cos(t)- EAet cos(t)|E| Ae2 cos(t2)]](http://img.homeworklib.com/images/79db7581-7675-4007-8d88-416096f523f0.latex?E%5BA%5E2e%5E%7B-%28t_1+t_2%29%7D%5Ccos%28t_1%29%5Ccos%28t_2%29%5D-E%5BAe%5E%7B-t_1%7D%5Ccos%28t_1%29%5DE%5BAe%5E%7B-t_2%7D%5Ccos%28t_2%29%5D?x-oss-process=image/resize,w_560)
Which equals ![e-(1tt) cos(t) cos(t2) E[A21 - (E[A]e cos(t1)) (E[A]e_t2 cos(t2)](http://img.homeworklib.com/images/53654114-12a2-4a18-8b95-7034e169e964.latex?e%5E%7B-%28t_1+t_2%29%7D%5Ccos%28t_1%29%5Ccos%28t_2%29E%5BA%5E2%5D-%5Cleft%20%28E%5BA%5D%20e%5E%7B-t_1%7D%5Ccos%28t_1%29%20%5Cright%20%29%5Cleft%20%28E%5BA%5D%20e%5E%7B-t_2%7D%5Ccos%28t_2%29%20%5Cright%20%29?x-oss-process=image/resize,w_560)
Which is ![EA (EIA)= Var(A) EA] = 202+ 102 - 500](http://img.homeworklib.com/images/0fe4e2c2-b3d9-4ba8-bc90-fc414426e9a1.latex?E%5BA%5E2%5D-%28E%5BA%5D%29%5E2%3D%5Ctext%7BVar%7D%28A%29%5CRightarrow%20E%5BA%5E2%5D%3D20%5E2+10%5E2%3D500?x-oss-process=image/resize,w_560)
So that ![e-(1tt) cos(t) cos(t2) E[A21 - (E[A]e cos(t1)) (E[A]e_t2 cos(t2)](http://img.homeworklib.com/images/3c192d93-ff2e-4d31-a2d5-1c2b3520ffdb.latex?e%5E%7B-%28t_1+t_2%29%7D%5Ccos%28t_1%29%5Ccos%28t_2%29E%5BA%5E2%5D-%5Cleft%20%28E%5BA%5D%20e%5E%7B-t_1%7D%5Ccos%28t_1%29%20%5Cright%20%29%5Cleft%20%28E%5BA%5D%20e%5E%7B-t_2%7D%5Ccos%28t_2%29%20%5Cright%20%29?x-oss-process=image/resize,w_560)
Which is (after multiplying out and simplifying)
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