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Generalisation. The mathematical expectation of the product of a number of independent random variables is equal to the product of their expectations. Symbolically, if X1, X, . X, are n independent r.v.'s, then E (X1, X2, ... X,) E (X1) E (X2) ... E (X„) E I x.) = I E (X), i.e., i = 1 provided all the expectations exist.

Generalisation. The mathematical expectation of the product of a number of independent random variables is equal to the product of their expectations. Symbolically, if X1, X, . X, are n independent r.v.'s, then E (X1, X2, ... X,) E (X1) E (X2) ... E (X„) E I x.) = I E (X), i.e., i = 1 provided all the expectations exist.

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

independent random variables is equal to the product of their expectations. Symbolically, if X1, X2, ..., X, are n independent r.v.'s, then Generalisation. The mathematical expectation of the product of a number of E (X1, X2, ... X„) = E (X1) E (X2) ... E (X„) E( I x) = 1 E (X), i.e., i = 1 i = 1 provided all the expectations exist.
Transcribed Image Text:independent random variables is equal to the product of their expectations. Symbolically, if X1, X2, ..., X, are n independent r.v.'s, then Generalisation. The mathematical expectation of the product of a number of E (X1, X2, ... X„) = E (X1) E (X2) ... E (X„) E( I x) = 1 E (X), i.e., i = 1 i = 1 provided all the expectations exist.
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