LetXbeadiscreterandom variablewithprobabilityfunctionp(x), g1(X),g2(X),g3(X),···,gk(X) be k functions of X. Then E[g1(X)+g2(X)+g3(X)+···+gk(X)] ≡ E[g1(X)]+E[g2(X)] +···+E[gk(X)] Proof for the case of k = 2

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 52E
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LetXbeadiscreterandom variablewithprobabilityfunctionp(x), g1(X),g2(X),g3(X),···,gk(X) be k functions of X. Then E[g1(X)+g2(X)+g3(X)+···+gk(X)] ≡ E[g1(X)]+E[g2(X)] +···+E[gk(X)] Proof for the case of k = 2

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