You went to a clinic to visit the doctor. There were 4 patients ahead of you in the waiting room. Their waiting times to meet the doctor were 12 minutes, 16 minutes, 12 minutes, and 8 minutes, respectively. Let X be the random variable for the waiting time of a patient. (a) Assuming X ~ Exponential (X) (i.e., an exponential distribution), use the maximum likelihood approach to estimate X from the waiting times of the 4 patients in front of you. (b) Based on your answer in part (a), what is the probability that your waiting time is less than 10 minutes? (c) Suppose the office has a sign that says the average wait time of a patient is about 10 minutes. Use this information to define the prior probability of A, i.e., A Exponential(). Based on this prior, calculate the value of λ using the maximum a posteriori (MAP) ap- proach. (d) Based on your answer in part (c), what is the probability that your waiting time is less than 10 minutes?
You went to a clinic to visit the doctor. There were 4 patients ahead of you in the waiting room. Their waiting times to meet the doctor were 12 minutes, 16 minutes, 12 minutes, and 8 minutes, respectively. Let X be the random variable for the waiting time of a patient. (a) Assuming X ~ Exponential (X) (i.e., an exponential distribution), use the maximum likelihood approach to estimate X from the waiting times of the 4 patients in front of you. (b) Based on your answer in part (a), what is the probability that your waiting time is less than 10 minutes? (c) Suppose the office has a sign that says the average wait time of a patient is about 10 minutes. Use this information to define the prior probability of A, i.e., A Exponential(). Based on this prior, calculate the value of λ using the maximum a posteriori (MAP) ap- proach. (d) Based on your answer in part (c), what is the probability that your waiting time is less than 10 minutes?
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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Transcribed Image Text:You went to a clinic to visit the doctor. There were 4 patients
ahead of you in the waiting room. Their waiting times to meet the doctor
were 12 minutes, 16 minutes, 12 minutes, and 8 minutes, respectively. Let
X be the random variable for the waiting time of a patient.
(a) Assuming X ~ Exponential (A) (i.e., an exponential distribution),
use the maximum likelihood approach to estimate A from the waiting
times of the 4 patients in front of you.
(b) Based on your answer in part (a), what is the probability that your
waiting time is less than 10 minutes?
(c) Suppose the office has a sign that says the average wait time of a
patient is about 10 minutes. Use this information to define the prior
probability of X, i.e., A ~ Exponential(). Based on this prior,
calculate the value of A using the maximum a posteriori (MAP) ap-
proach.
(d) Based on your answer in part (c), what is the probability that your
waiting time is less than 10 minutes?
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