Generalisation. The mathematical expectation of the sum of n random variables is equal to the suni of their expectations, provided all the expectations exist. Symbolically, if X1, X2, ., X, are random variables them E (X1 + X2+ ... + X,) = E (X1) + E (X2) + + E (X,) 11 E(E x = 2 E (X), if all the expectations exist. E E (X;), if all the expectations exist. i = 1 %3D or i = 1

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Matrices
Section2.5: Markov Chain
Problem 16E: Consumer Preference In a population of 100,000 consumers, there are 20,000 users of Brand A, 30,000...
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Prove the theorem

Generalisation. The mathematical expectation of the sum of n random variables is equal
to the sun of their expectations, provided all the expectations exist. Symbolically, if X1, X2,
X, are random variables then
E (X1+ X2 + ...
+ X„) = E (X1) + E (X2) + ...
+ E (X„)
%3D
11
E( Σ x ) -Σ Ε(%),
2 E (X;), if all the expectations exist.
i = 1
or
i = 1
Transcribed Image Text:Generalisation. The mathematical expectation of the sum of n random variables is equal to the sun of their expectations, provided all the expectations exist. Symbolically, if X1, X2, X, are random variables then E (X1+ X2 + ... + X„) = E (X1) + E (X2) + ... + E (X„) %3D 11 E( Σ x ) -Σ Ε(%), 2 E (X;), if all the expectations exist. i = 1 or i = 1
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