Form the covariance function 



where E is the expected value over the ensemble for any fixed x,y,t. 

 Note that ^ 



is a constant with respect to the expected value. 



Consider the following problem. Let u be a random variable with 

 uniform probability density function 



Define a random variable Z = e . The expected value of Z is defined 



as 



CK. 



Considering the random variable nature of the phase Zira as described 

 following Equation (2.17) at the end of Section 2, and applying the above 

 notion to the cross product terms of R(X,Y,T) we obtain 



R(XYT) =^[t*f>{i%ir(tyii-y^Y-^^T)) + 



10 



