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Please help me with the first problem

Please help me with the first problem

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Please help me with the first problem

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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