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

#### johnsmith

##### New member
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).

#### mmm4444bot

##### Super Moderator
Staff member
This is a tutoring forum; we don't complete student assignments.

Please read the forum guidelines, and then show what you've tried or thought about (so far).