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(2) = { (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.

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter6: Exponential And Logarithmic Functions
Section6.8: Fitting Exponential Models To Data
Problem 3TI: Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to...
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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
-x/11
P(x) = {
p(a
(a) In order to be a probability density function, we require
| p(x) dr
= 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) dr. Find the
probability that
i. you wait between 5 ad 8 minutes for
your
lunch.
ii. you wait at least 15 minutes for your lunch.
(c) The mea, or average, wait time is given by
xp(x) dx.
-0∞
Calculate the mean wait time for lunch at the HUB.
(d) The median m wait time is defined by the equation
m
| p(x) = 0.5.
Calculate the median wait time.
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 -x/11 P(x) = { p(a (a) In order to be a probability density function, we require | p(x) dr = 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) dr. Find the probability that i. you wait between 5 ad 8 minutes for your lunch. ii. you wait at least 15 minutes for your lunch. (c) The mea, or average, wait time is given by xp(x) dx. -0∞ Calculate the mean wait time for lunch at the HUB. (d) The median m wait time is defined by the equation m | p(x) = 0.5. Calculate the median wait time.
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