(a) If you have already been waiting for 10 minutes (i.e. it is 12:10pm) and the first bus has not yet come, what is the probability that you will have to wait at least 15 additional minutes? (b) Repeat part (a) under the assumption that the number of minutes from noon until the first bus is uniformly distributed over [0, 40]. (c) Explain how the answers to (a) and (b) relate to whether exponential and uniform random variables are memoryless.
(a) If you have already been waiting for 10 minutes (i.e. it is 12:10pm) and the first bus has not yet come, what is the probability that you will have to wait at least 15 additional minutes? (b) Repeat part (a) under the assumption that the number of minutes from noon until the first bus is uniformly distributed over [0, 40]. (c) Explain how the answers to (a) and (b) relate to whether exponential and uniform random variables are memoryless.
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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Hello! I need help with the following problem. Thank you in advance..!
![One day at noon, you have a sudden craving for a California burrito from the Taco Stand, and
you decide to take the bus from campus into town. Starting at noon, suppose that the number
of minutes until the first bus arrives is an exponential random variable with parameter 1/20.
(a) If you have already been waiting for 10 minutes (i.e. it is 12:10pm) and the first bus has not
yet come, what is the probability that you will have to wait at least 15 additional minutes?
(b) Repeat part (a) under the assumption that the number of minutes from noon until the first bus
is uniformly distributed over [0, 40].
(c) Explain how the answers to (a) and (b) relate to whether exponential and uniform random
variables are memoryless.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F25ecc335-25be-4ebd-8f8c-629ee64b2629%2F9b59deed-e328-4d01-bf93-79650dcdb327%2Fbdyyvk_processed.png&w=3840&q=75)
Transcribed Image Text:One day at noon, you have a sudden craving for a California burrito from the Taco Stand, and
you decide to take the bus from campus into town. Starting at noon, suppose that the number
of minutes until the first bus arrives is an exponential random variable with parameter 1/20.
(a) If you have already been waiting for 10 minutes (i.e. it is 12:10pm) and the first bus has not
yet come, what is the probability that you will have to wait at least 15 additional minutes?
(b) Repeat part (a) under the assumption that the number of minutes from noon until the first bus
is uniformly distributed over [0, 40].
(c) Explain how the answers to (a) and (b) relate to whether exponential and uniform random
variables are memoryless.
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