Suppose that the number of customers visiting a fast food restaurant in a given time interval I
Question:
Suppose that the number of customers visiting a fast food restaurant in a given time interval I is N ∼ Poisson(μ). Assume that each customer purchases a drink with probability p, independently from other customers, and independently from the value of N. Let X be the number of customers who purchase drinks in that time interval. Also, let Y be the number of customers that do not purchase drinks; so X +Y = N.
a. Find the marginal PMFs of X and Y .
b. Find the joint PMF of X and Y .
c. Are X and Y independent?
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a First note that Rx Ry 0 1 2 Also given N n X is a sum of n independent Bern...View the full answer
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Related Book For 
Introduction To Probability Statistics And Random Processes
ISBN: 9780990637202
1st Edition
Authors: Hossein Pishro-Nik
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