Physicsal meaning of Expectation of two variables

[persist911]

I have a problem understanding why I need the expectation of two variable which are dependent. What is the physical meaning of this E[xy]. I know that E[X] is the likelihood f finidng say a particle from a experiment repreated N time atthe same place. What Kind of physical meaning exist of two variable.

 

[A. Neumaier]

I have a problem understanding why I need the expectation of two variable which are dependent. What is the physical meaning of this E[xy]. I know that E[X] is the likelihood f finidng say a particle from a experiment repreated N time at the same place. What Kind of physical meaning exist of two variable.

If x and y are two random variables and f(x,y) is any expression in x and y then E[f(x,y)] is the limiting value of the sample mean of the values f(x_i,y_i) of N independently sampled points (x_i,y_i) as N gets arbitrarily large.