Cafe Espresso is a very popular coffee shop at UCI. The owner of Cafe Espresso notices that on average85 customers order coffee on a given day. Let X be the number of customers who order coffee at CafeEspresso, and we will assume that E[X] = 85.(a) Assume that the expected value of X is a constant daily rate and the number of customers whoorder coffee at Cafe Espresso is independent of any other day. What is the distribution of X?Justify your answer.(b) Using the distribution from part (a), what is the Mean and Standard Deviation of the number ofcustomers who order coffee at cafe express in a give day.(c) Using the distributing from part (a), what is the probability that at least 81 customers order coffeeat Cafe Espresso in a given day?(d) Suppose that the number of costumers who order coffee at Cafe Espresso in any increment of timeis independent of the number of costumer who order coffee at Cafe Espresso in any other incrementof time. Suppose that Cafe Espresso only opens between 6:00am and 3:00pm. 1) What is theprobability that at least 11 costumer order coffee in one hour during a given day? 2) What is theprobability that no costumer order coffee in one hour during a given day?(e) Using the assumption from above, what is the expected number of customers who order coffee atCafe Espresso in one quarter? Assume that each day is independent of the other days and thatthere are 70 days in a quarter.

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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