ion 3 The exponential distribution is a probability distribution that describes the time needed for a process to change state. Suppose the number of minutes you wait in line for lunch at the HUB has the probability density function x > 0 x < 0 Ce¬²/11 p(z) = { (a) In order to be a probability density function, we require p(x) dx = 1. Use this to solve for the normalization constant C. (b) The probability that the wait time is between a and b minutes is given by p(x) dx. Find the probability that i. you wait between 5 and 8 minutes for your lunch. ii. you wait at least 15 minutes for your lunch.
ion 3 The exponential distribution is a probability distribution that describes the time needed for a process to change state. Suppose the number of minutes you wait in line for lunch at the HUB has the probability density function x > 0 x < 0 Ce¬²/11 p(z) = { (a) In order to be a probability density function, we require p(x) dx = 1. Use this to solve for the normalization constant C. (b) The probability that the wait time is between a and b minutes is given by p(x) dx. Find the probability that i. you wait between 5 and 8 minutes for your lunch. ii. you wait at least 15 minutes for your lunch.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.6: Quadratic Functions
Problem 38E
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Transcribed Image Text:Question 3 The exponential distribution is a probability distribution that describes the time needed for a process to
change state. Suppose the number of minutes you wait in line for lunch at the HUB has the probability
density function
Ce-¤/11
x > 0
p(x) = {
x < 0
(a) In order to be a probability density function, we require
| p(a)
1.
dx =
Use this to solve for the normalization constant C.
(b) The probability that the wait time is between a and b minutes is given by
p(x) dx. Find the
probability that
i. you wait between 5 and 8 minutes for your lunch.
ii. you wait at least 15 minutes for your
lunch.
(c) The mean, or average, wait time is given by
x =
dx.
-00
Calculate the mean wait time for lunch at the HUB.
(d) The median m wait time is defined by the equation
| p(x) = 0.5.
Calculate the median wait time.
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