A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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Chapters: Normal and Exponential random variables.
Q: For each of the following descriptions of a random variable,
indicate whether it can best be modeled by binomial,
geometric, uniform, exponential or normal. Also, answer the
associated question.
a. Let Y be the random variable that counts the number of sixes
which occur when a die is tossed 10 times. Wht type of random
variable is Y? What is $P(Y=3)? What is the expected number of
sixes?
b. Suppose a stop light has a red light that lasts for 60 seconds a
green light that lasts for 30 seconds and a yellow light that lasts
for 5 seconds. When you first observe the stop light, it is red. Let
X denote the time until the light turns green. What type of rv
would be used to model X? What is the mean?
c. Customers arrive at a teller's window at a uniform rate 5 per
hour. Let X be the length in minutes of time that the teller has to
wait until they see their first customer after starting their shift.
What type of rv is X? What is its mean? Find the probability that
the teller waits less than 10 minutes for their first customer.
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Transcribed Image Text:Chapters: Normal and Exponential random variables. Q: For each of the following descriptions of a random variable, indicate whether it can best be modeled by binomial, geometric, uniform, exponential or normal. Also, answer the associated question. a. Let Y be the random variable that counts the number of sixes which occur when a die is tossed 10 times. Wht type of random variable is Y? What is $P(Y=3)? What is the expected number of sixes? b. Suppose a stop light has a red light that lasts for 60 seconds a green light that lasts for 30 seconds and a yellow light that lasts for 5 seconds. When you first observe the stop light, it is red. Let X denote the time until the light turns green. What type of rv would be used to model X? What is the mean? c. Customers arrive at a teller's window at a uniform rate 5 per hour. Let X be the length in minutes of time that the teller has to wait until they see their first customer after starting their shift. What type of rv is X? What is its mean? Find the probability that the teller waits less than 10 minutes for their first customer.
d. A coin is tossed until a head is observed. Let X denote the total
number of tails observed during the experiment. What type of rv
is X? What is its mean? Find P(X < 3).
f. Let X be the recorded body temperature of a healthy adult in
degrees Fahrenheit. What type of rv is X? Estimate its mean and
standard deviation, based on your knowledge of body
temperatures.
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Transcribed Image Text:d. A coin is tossed until a head is observed. Let X denote the total number of tails observed during the experiment. What type of rv is X? What is its mean? Find P(X < 3). f. Let X be the recorded body temperature of a healthy adult in degrees Fahrenheit. What type of rv is X? Estimate its mean and standard deviation, based on your knowledge of body temperatures.
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