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Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
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Linearity of expectation SE S Suppose that X and Y are random variables on the same space of outcOmes Then E(X + Y) = E(X)+ E(Y). Why? r.v. We prove it for discrete random variables (X+y) G). valne of X+Y when outame is s • Let S be the space of outcomes for X and Y Then E(X + Y) = ESES(X+ Y)(s) = EX(s) + Y(s)): EsX(s) + Es?Y(s) = E(X)+ E(Y) 1 Problem: Prove that E(cX) = cE(X) for constants c and discrete random variables X SES • Problem: Prove that E(E X;) = E, E(X;) random variables X1, . . . , Xk È CaX +bY)= E(aX)+E(bY)= fofdiscreteE(M i=1 discréte
Transcribed Image Text:Linearity of expectation SE S Suppose that X and Y are random variables on the same space of outcOmes Then E(X + Y) = E(X)+ E(Y). Why? r.v. We prove it for discrete random variables (X+y) G). valne of X+Y when outame is s • Let S be the space of outcomes for X and Y Then E(X + Y) = ESES(X+ Y)(s) = EX(s) + Y(s)): EsX(s) + Es?Y(s) = E(X)+ E(Y) 1 Problem: Prove that E(cX) = cE(X) for constants c and discrete random variables X SES • Problem: Prove that E(E X;) = E, E(X;) random variables X1, . . . , Xk È CaX +bY)= E(aX)+E(bY)= fofdiscreteE(M i=1 discréte
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