Price's Theorem
Consider a bivariate normal distribution in variables 
and 
with covariance
 |
(1)
|
and an arbitrary function 
. Then the expected value of the random variable 
 |
(2)
|
satisfies
 |
(3)
|
REFERENCES:
McMahon, E. L. "An Extension of Price's Theorem." IEEE Trans. Inform. Th. 10, 168-171, 1964.
Papoulis, A. "Price's Theorem and Join Moments." Probability, Random Variables, and Stochastic Processes, 2nd ed. New York: McGraw-Hill, pp. 226-228, 1984.
Price, R. "A Useful Theorem for Non-Linear Devices Having Gaussian Inputs." IEEE Trans. Inform. Th. 4, 69-72, 1958.
