Suppose you open a shop in UTC plaza and you need to estimate the number of customers. During the lunch time, the number of students coming to UTC plaza in a time period is a random variable of Poisson distribution, X ~ Poisson(\), \ > 0. Among these X students, you observe that each student will visit your shop with probability p independently, where 0 < p < 1. Let Y be the number of students that visit your shop (in a time period) and Z be the number of the student who does not visit. (Note: To check you understand the question correctly, X should be equal to Y + Z by definition.) (a) Compute joint distribution of (Y, Z). (b) Show Y, Z are independent.

Suppose you open a shop in UTC plaza and you need to estimate the number of customers. During the lunch time, the number of students coming to UTC plaza in a time period is a random variable of Poisson distribution, X ~ Poisson(\), \ > 0. Among these X students, you observe that each student will visit your shop with probability p independently, where 0 < p < 1. Let Y be the number of students that visit your shop (in a time period) and Z be the number of the student who does not visit. (Note: To check you understand the question correctly, X should be equal to Y + Z by definition.) (a) Compute joint distribution of (Y, Z). (b) Show Y, Z are independent.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section: Chapter Questions

Problem 27T

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