4. Students arrive at a tutoring center to a Poisson process with a rate of 10 per hour. (a) What is the probability that the second arrival is observed less than 15 minutes after the first arrival? (b) What is the probability that the third arrival is observed less than 10 minutes after the second arrival if it has not yet been observed 5 minutes after the second arrival? (c) What is the probability that more than 20 minutes is required for the third arrival? (d) Suppose a volunteer working at the center has a 6-hour shift. Compute the expected value and the variance for the number of students who would arrive during her shift.
4. Students arrive at a tutoring center to a Poisson process with a rate of 10 per hour. (a) What is the probability that the second arrival is observed less than 15 minutes after the first arrival? (b) What is the probability that the third arrival is observed less than 10 minutes after the second arrival if it has not yet been observed 5 minutes after the second arrival? (c) What is the probability that more than 20 minutes is required for the third arrival? (d) Suppose a volunteer working at the center has a 6-hour shift. Compute the expected value and the variance for the number of students who would arrive during her shift.
A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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![4. Students arrive at a tutoring center to a Poisson process with a rate of 10 per hour.
(a) What is the probability that the second arrival is observed less than 15 minutes after the first
arrival?
(b) What is the probability that the third arrival is observed less than 10 minutes after the second
arrival if it has not yet been observed 5 minutes after the second arrival?
(c) What is the probability that more than 20 minutes is required for the third arrival?
(d) Suppose a volunteer working at the center has a 6-hour shift. Compute the expected value and
the variance for the number of students who would arrive during her shift.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F377b8d6e-0b43-439e-adad-4590c50894c7%2F3ab0aada-0078-4711-8dba-029c92b1136d%2Fd768nw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4. Students arrive at a tutoring center to a Poisson process with a rate of 10 per hour.
(a) What is the probability that the second arrival is observed less than 15 minutes after the first
arrival?
(b) What is the probability that the third arrival is observed less than 10 minutes after the second
arrival if it has not yet been observed 5 minutes after the second arrival?
(c) What is the probability that more than 20 minutes is required for the third arrival?
(d) Suppose a volunteer working at the center has a 6-hour shift. Compute the expected value and
the variance for the number of students who would arrive during her shift.
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