Please help me with the first problem
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
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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