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?
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.3: Binomial Probability
Problem 2E: If a binomial experiment has probability p success, then the probability of failure is...
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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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