You arrive at CS109 Office Hours to find that 5 CS109 CAs—Yonatan, Will, Kathleen, Jacob, and Naomi—are all present, and each is working with some fellow CS109 student of yours. You notice there are nine other students in front of you in the queue and no one is behind you. It looks like you'll be the last of 10 students to be helped. We'll assume the time each CA spends with a student can be modeled as an Exponential random variable such that, on average, each CA finishes helping precisely 6 students every hour. As a CA finishes helping a student, they immediately start helping the next student in line and remove them from the queue. Question: What is the probability that Yonatan and Naomi collectively end up helping all nine of the students ahead of you in line? Present your answer out to six decimal places, the first three of which should be zero. Hint: Rely on the memoryless property of the Exponential distribution.

You arrive at CS109 Office Hours to find that 5 CS109 CAs—Yonatan, Will, Kathleen, Jacob, and Naomi—are all present, and each is working with some fellow CS109 student of yours. You notice there are nine other students in front of you in the queue and no one is behind you. It looks like you'll be the last of 10 students to be helped. We'll assume the time each CA spends with a student can be modeled as an Exponential random variable such that, on average, each CA finishes helping precisely 6 students every hour. As a CA finishes helping a student, they immediately start helping the next student in line and remove them from the queue. Question: What is the probability that Yonatan and Naomi collectively end up helping all nine of the students ahead of you in line? Present your answer out to six decimal places, the first three of which should be zero. Hint: Rely on the memoryless property of the Exponential distribution.

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

In her last semester at SPC, Polly Hedron needs to take Statistics, Composition 2, and Ethics. Because Polly is registering early, she has 13 choices for her section of Statistics, 15 choices for her section of Composition, and 20 choices for her section of Ethics. From how many possible schedules can Polly choose?
The amount of contaminants that are allowed in food products is determined by the FDA (Food and Drug Administration). Common contaminants in cow milk include feces, blood, hormones, and antibiotics. Suppose you work for the FDA and are told that the current amount of somatic cells (common name "pus") in 1 cc of cow milk is currently 750,000 (note: this is the actual allowed amount in the US!). You are also told the standard deviation is 62000 cells. The FDA then tasks you with checking to see if this is accurate. You collect a random sample of 45 specimens (1 cc each) which results in a sample mean of 762004 pus cells. Use this sample data to create a sampling distribution. Assume that the population mean is equal to the FDA's legal limit and see what the probability is for getting your random sample. a. Why is the sampling distribution approximately normal? b. What is the mean of the sampling distribution? c. What is the standard deviation of the sampling distribution? d. Assuming…
I already have a,b,c and d. I just need help on E, F, G, and H
Part 4: Suppose that 53 of the 55 Computer Science students of San Sebastian College, Manila are taking at least one of the mathematics subjects Algebra, Trigonometry and Calculus. See the figure below for more details: 24 taking Algebra, 26 taking Trigonometry, 20 taking Calculus, 5 taking Algebra and Trigonometry, 7 taking Algebra and Calculus, 8 taking Trigonometry and Calculus. a. Find the number of students who are taking all three mäthematics subjects. b. Fill in the correct number of students in each of the eight regions of the Venn diagram. c. Determine the number of students who are not taking any of the three mathematics subjects? d. How many students are taking Algebra as their only mathematics subject? e. How many students were taking Calculus and Trigonometry but not Algebra?
The board of an Internet startup company has fifteen members. If one person is to be in charge of researchnbspand another in charge of accounting, in how many ways can these two positions be filled?
The owner of a stereo store wants to advertise that he has many different sound systems in stock. The store carries 6 different CD players, 10 different receivers, and 9 different speakers. Assuming a sound system consists of one of each, how many different sound systems can he advertise?