Suppose that arrivals to a coffee shop follow a Poisson process with average rate of one customer every 5 minutes. What are the probabilities of (a) no customers in 5 minutes; (b) exactly one customer in a minute; (c) exactly two customers in 2 minutes; and (d) at least two customers in 10 minutes?

Suppose that arrivals to a coffee shop follow a Poisson process with average rate of one customer every 5 minutes. What are the probabilities of (a) no customers in 5 minutes; (b) exactly one customer in a minute; (c) exactly two customers in 2 minutes; and (d) at least two customers in 10 minutes?

Name: Suppose that arrivals to a coffee shop follow a Poisson process with a
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: Suppose that arrivals to a coffee shop follow a Poisson process with average rate of one customer every 5 minutes. What are the probabilities of (a) no customers in 5 minutes; (b) exactly one customer in a minute; (c) exactly two customers in 2 minut

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...

See similar textbooks

Similar questions

A machine can be in one of four states: ‘running smoothly’ (state 1), ‘running but needs adjustment’ (state 2), ‘temporarily broken’ (state 3), and ‘destroyed’ (state 4). Each morning the state of the machine is recorded. Suppose that the state of the machine tomorrow morning depends only on the state of the machine this morning subject to the following rules. If the machine is running smoothly, there is 1% chance that by the next morning it will have exploded (this will destroy the machine), there is also a 9% chance that some part of the machine will break leading to it being temporarily broken. If neither of these things happen then the next morning there is an equal probability of it running smoothly or running but needing adjustment. If the machine is temporarily broken in the morning then an engineer will attempt to repair the machine that day, there is an equal chance that they succeed and the machine is running smoothly by the next day or they fail and cause the machine to…
There are three groceries shops operat in a rural area: Maharaja, Ahmed Emporium, and Quick Stop Groceries. Assume that the transition probabilities are as follows: To From Maharaja Quick Stop Ahmed's Maharaja Store 0.81 0.07 Ahmed's Emporium 0.1 0.84 Quick Stop Groceries 0.09 0.05 Calculate =Maharaja's steady-state probability Use 4 digits after decimal point - for example ( answer should be similar to 0.1234)
5. Assume the below life table was constructed from following individuals who were diagnosed with a slow-progressing form of prostate cancer and decided not to receive treatment of any form. Calculate the survival probability at year 2 using the Kaplan-Meir approach and interpret the results. Time in Years Number at Risk, Nt Number of Deaths, Dt Number Censored, Ct Survival Probability 0 20 1 1 20 3 2 17 1 3 16 2 1 The probability of surviving 2 years after being diagnosed with a slow-progressing form of prostate cancer is .85. The probability of surviving 2 years after being diagnosed with a slow-progressing form of prostate cancer is .85 for the individuals being followed in this study. The probability of surviving 2 years after being diagnosed with a slow-progressing form of prostate cancer is .85 for individuals who decided against all forms of treatment. The probability of surviving 2 years after…
4. A merchant stocks a certain perishable item. He knows that on any given day, he will have a demand for either 2, 3, or 4 of this items with probabilities 0.1, 0.4 and 0.5 respectively. What is the average daily demand?
Imagine you have three coins: one is fair, one is biased (twice as likely to be heads as tails), the third is also biased (twice as likely to be tails as heads). You pick one of the three coins at random, and flip it 20 times. How should you decide which coin you are holding, based on the results, to maximize your probability of being correct?
One student is selected at random from a group of 200 known to consist of 140 full-time (80 female and 60 male) student and 60 part-time (40 female and 20 male) students. Event A is "the student selected is full-time" and event C is "the student selected is female". (a) Are events A and C independent? (b) Find the probability of one student selected is full-time, that should be female.
1. A machine can be in one of four states: 'running smoothly' (state 1), 'running but needs adjustment' (state 2), 'temporarily broken' (state 3), and 'destroyed' (state 4). Each morning the state of the machine is recorded. Suppose that the state of the machine tomorrow morning depends only on the state of the machine this morning subject to the following rules. • If the machine is running smoothly, there is 1% chance that by the next morning it will have exploded (this will destroy the machine), there is also a 9% chance that some part of the machine will break leading to it being temporarily broken. If neither of these things happen then the next morning there is an equal probability of it running smoothly or running but needing adjustment. • If the machine is temporarily broken in the morning then an engineer will attempt to repair the machine that day, there is an equal chance that they succeed and the machine is running smoothly by the next day or they fail and cause the machine…
1.A family wishes to adopt 4 pets from a total of 13 dogs and 7 cats available at an animal shelter. The variable "x" being measured is the number of dogs. Show the probability distribution table, using 3 columns: one for x, one for P(x), and one for x*P(x). The second column should show calculations using C(Dt). 2. A student forum at a high school needs to elect 5 people from 10 Grade 11 students and 15 Grade 12 students who are available. The variable"" being measured is the number of Grade 12 students. Show the probability distribution table, using 3 columns: one for x, one for P(x), and one for x*P(x). The second column should show calculations involving C(Dt).
5. A distributed system contains 4 computers. What is the probability of its failure in one year, if probability of failure of the computers in this period are 0.1, 0.2, 0.3, 0.4?
1. A machine can be in one of four states: 'running smoothly' (state 1), 'running but needs adjustment' (state 2), 'temporarily broken' (state 3), and 'destroyed' (state 4). Each morning the state of the machine is recorded. Suppose that the state of the machine tomorrow morning depends only on the state of the machine this morning subject to the following rules. • If the machine is running smoothly, there is 1% chance that by the next morning it will have exploded (this will destroy the machine), there is also a 9% chance that some part of the machine will break leading to it being temporarily broken. If neither of these things happen then the next morning there is an equal probability of it running smoothly or running but needing adjustment. • If the machine is temporarily broken in the morning then an engineer will attempt to repair the machine that day, there is an equal chance that they succeed and the machine is running smoothly by the next day or they fail and cause the machine…
3. A hacker breaking into a computer system has a 15% chance of breaking into a system in 3 minutes, a 35% chance after 8 minutes, and a 50% chance after 30 minutes. What is the expected time it will take the hacker to get in?
Suppose A, B and C are events such that P(A): = 0.46, P(B): = P(BNC) = P(ANC) = 0.16 and P(AnBnC) = 0.06. (a) Are events A and B mutually exclusive? Why? (b) Find P((An BNC)) (c) Find P((AUBUC)) 0.51, P(C) = 0.41, P(An B) =