Probability density function for Z(t)=Xcost+Ysint, given E[X]=E[Y]=0, D[X]=D[Y]=1

[johnsmith]

Let Z(t)=Xcost+Ysint, where X and Y are mutually independent Gaussian random variables, and E[X]=E[Y]=0, D[X]=D[Y]=1.
Please give:
(1) Z(t)’s probability density function;
(2) The joint probability density function of Z(t1) and Z(t2).

 

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