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...

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