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 randomvariable of Poisson distribution, X ~ Poisson(\), \ > 0. Among these X students, you observe thateach student will visit your shop with probability p independently, where 0 < p < 1. Let Y be thenumber of students that visit your shop (in a time period) and Z be the number of the student whodoes 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.

The probability mass function (pmf) of Y given X = n is:P(Y = k | X = n) = (n choose k) * p^k *…

Answered: Suppose you open a shop in UTC plaza…

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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