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neore 5.3. If tlhe ràndóm variables X and Y are stochastically mdependent, then for all possible selections of the corresponding pairs of real numbers (a, b,), (a,, b,) where a;

neore 5.3. If tlhe ràndóm variables X and Y are stochastically mdependent, then for all possible selections of the corresponding pairs of real numbers (a, b,), (a,, b,) where a;

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 5-3. If the random variables X and Y are stochastically independent, then for all possible selections of the corresponding pairs of real numbers (a,, b¡), (a2, b2) where a; < b; for all i = 1, 2 and where the values ± ∞ are allowed, the events (a, < X <b;) and (a2 < Y <b2) are independent, i.e., P (a1 < X < b1) n (a2< Y< b2)} = P(a1 < X < bj) P (a2 < Y< bz) CS Scanned with CamScanner
Transcribed Image Text:! Theorem 5-3. If the random variables X and Y are stochastically independent, then for all possible selections of the corresponding pairs of real numbers (a,, b¡), (a2, b2) where a; < b; for all i = 1, 2 and where the values ± ∞ are allowed, the events (a, < X <b;) and (a2 < Y <b2) are independent, i.e., P (a1 < X < b1) n (a2< Y< b2)} = P(a1 < X < bj) P (a2 < Y< bz) CS Scanned with CamScanner
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