Monitor three customers purchasing smartphones sat the Phonesmart store and observe whether each buys an Apricot phone for $450 or a Banana phone for $300. The random variable N is the number of customers purchasing an Apricot phone. Assume N has the PMF below. Find the ecpected value E(N) by using the following: a) The theorem: Given a rondom variable X with PMF PX(x) and the derived random variable Y = g(X), the expected value of Y is E[Y] = μY = Σ[ g(x)*PX(x) ] b) The definition: The expected value of X is E[X] = μX = Σ[ x*PX(x) ]

A First Course in Probability (10th Edition)
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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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Monitor three customers purchasing smartphones sat the Phonesmart store and observe whether each buys an Apricot phone for $450 or a Banana phone for $300. The random variable N is the number of customers purchasing an Apricot phone. Assume N has the PMF below. Find the ecpected value E(N) by using the following:

a) The theorem: Given a rondom variable X with PMF PX(x) and the derived random variable Y = g(X), the expected value of Y is E[Y] = μY = Σ[ g(x)*PX(x) ]

b) The definition: The expected value of X is E[X] = μX = Σ[ x*PX(x) ]

PN (n) =
0.4 n=0,
0.2 n=1,2,3,
0
otherwise.
Transcribed Image Text:PN (n) = 0.4 n=0, 0.2 n=1,2,3, 0 otherwise.
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