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Statistics / Probability and Statistical Inference 9 / Chapter 5.4 / Problem 5.4-20

Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman

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The time X in minutes of a visit to a cardiovascular disease specialist by a patient is

Chapter 5, Problem 5.4-20

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QUESTION:

The time X in minutes of a visit to a cardiovascular disease specialist by a patient is modeled by a gamma pdf with = 1.5 and = 10. Suppose that you are such a patient and have four patients ahead of you. Assuming independence, what integral gives the probability that you will wait more than 90 minutes?

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QUESTION:

The time X in minutes of a visit to a cardiovascular disease specialist by a patient is modeled by a gamma pdf with = 1.5 and = 10. Suppose that you are such a patient and have four patients ahead of you. Assuming independence, what integral gives the probability that you will wait more than 90 minutes?

ANSWER:

Problem 5.4.20

The time X in minutes of a visit to a cardiovascular disease specialist by a patient is modeled by a gamma pdf with and . Suppose that you are such a patient and have four patients ahead of you. Assuming independence, what integral gives the probability that you will wait more than 90 minutes?

Step by Step Solution

Step 1 of 3

Suppose are the observations of a random sample from the distribution with the moment-generating function, then the moment-generating function of is.

The moment-generating function of each , , is,

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