Summary: Price’s remarkable theorem on Gaussian random variables was published in 1958 [IRE Trans. Inform. Theory 4, 69–72 (1958; Zbl 0108.30605)] and distinguished by the Information Theory Society Golden Jubilee Paper Award in 1988. Nowadays, this theorem remains an important tool used extensively in a wide spectrum of engineering problems, such as those appearing in signal processing, radio and space sciences, as well as information theory and astrophysics. In this paper, Price’s theorem is applied to the investigation of possible uncorrelatedness for powers of Gaussian random variables. For zero-mean Gaussian variables the only two possible uncorrelatedness sets has been identified and presented.
The study aims to bring into spotlight the celebrated theorem usually disregarded in standard Probability and Statistics courses as well as to initiate further interest in the theorem by demonstrating a series of new applications.