Let X and Y are statistically independent Gaussian distributed random variables, each with zero mean and unit variance Define the Gaussian process Z (t) Z cos (2t) Y sin (2t) (a) Determine the joint probability density function of the random variables Z (t1) and Z (i2) obtained by observing Z (t) a...

a The expected value of Zt is EZt cos2t EX sin2t EY Since EX E Y 0 we deduce that EZ 0 Similarly w ...

Let X and Y are statistically independent Gaussian-distributed random variables, each with zero mean and unit variance.

Question:

Let X and Y are statistically independent Gaussian-distributed random variables, each with zero mean and unit variance. Define the Gaussian process Z (t) = Z cos (2πt) + Y sin (2πt)

(a) Determine the joint probability density function of the random variables Z (t1) and Z (i2) obtained by observing Z (t) at times t= and t2 respectively.

(b) Is the process Z (t) stationary? Why?