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Theorem 5.2. Two random variables X and Y with joint p.d.f. f(x, y) are stochastically independent if and only if fx, y(x, y) can be expressed as the product of a non-negative function of x alone and a non-negative function of y alone, i.e., if fxy(x, y ) = lix (x). kỵ (y), where h (.) 20 and k (.) 2 0.

Theorem 5.2. Two random variables X and Y with joint p.d.f. f(x, y) are stochastically independent if and only if fx, y(x, y) can be expressed as the product of a non-negative function of x alone and a non-negative function of y alone, i.e., if fxy(x, y ) = lix (x). kỵ (y), where h (.) 20 and k (.) 2 0.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Prove the theorem

Theorem 5-2. Two random variables X and Y with joint p.d.f. f(x, y) are stochastically independent if and only if fx, y(x, y) can be expressed as the product of a non-negative function of x alone and a non-negative function of y alone, i.c., if fxy(x, y ) = lix (x). kỵ (y), where h (.) 20 and k (.) 20. CS Scanned with CamScanner
Transcribed Image Text:Theorem 5-2. Two random variables X and Y with joint p.d.f. f(x, y) are stochastically independent if and only if fx, y(x, y) can be expressed as the product of a non-negative function of x alone and a non-negative function of y alone, i.c., if fxy(x, y ) = lix (x). kỵ (y), where h (.) 20 and k (.) 20. CS Scanned with CamScanner
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