The following time averages are of particular interest

     (a) Time-averaged mean

      
      

     (b) Time-averaged autocorrelation function

      
      
  Note that, and are functions of random variables and are governed by respective probability   distributions. However, determination of these distribution functions is difficult and we shall discuss the behaviour of   these averages in terms of their mean and variances. We shall further assume that the random processes   and are WSS.