Chapter 4 - Continuous Random Variables and Probability Distributions
SHORT ANSWER
1. Let X denote the amount of time for which a book on 2-hour reserve at a college-library is checked out by a
randomly selected student and suppose that X
Calculate the following probabilities:
a.
b.
ANS:
a.
b.
PTS: 1
2. A college professor always finishes his lectures within 2 minutes after the bell rings to end the period and the end of
the lecture. Let X = the time that elapses between the bell and the end of the lecture and suppose the pdf of X is
, a. Find the value of k. [Hint: Total area under the graph of f(x) is 1.]
b. What is the probability that the lecture ends within 1minutes of the bell ringing?
c. What is the probability that the lecture continues beyond the bell for between 60 and 90 seconds?
d. What is the probability that the lecture continues for at least 90 seconds beyond the bell?
ANS:
a.
b.
c.
d.
PTS: 1
3. The time X (minutes) for a lab assistant to prepare the equipment for a certain experiment is believed to have a
uniform distribution with A = 20 and B = 30.
a. Write the pdf of X and sketch its graph.
b. What is the probability that preparation time exceeds 27 minutes?
c. Find the preparation mean time, then calculate the probability that preparation is within 2 minutes of the mean
time?
d. For any a such that 20 < a < a + 2 < 30, what is the probability that preparation time is between a and a + 2
minutes?
ANS:
a.
b.
c.
25 2 is from 23 to 27 minutes:
d. since the interval has length 2.
PTS: 1
4. “Time headway” in traffic flow is the elapsed time between the time that one car finishes passing a fixed point and
the instant that the next car begins to pass that point. Let X = the time headway for two randomly chosen
consecutive cars on a freeway during a period of heavy flow. The following pdf of X is
, What is the probability that the time headway is
a. At most 6 seconds?
b. At least 6 seconds?
c. At most 5 seconds?
d. Between 5 and 6 seconds?
ANS:
a.
b.
c.
d.
PTS: 1
5. The cdf of checkout duration X for a book on a 2-hour reserve at a college library is given by:
Use this cdf to compute the following:
a.
b.
c.
d. The median checkout duration
e.
ANS:
a.
b.
c.
d.
SHORT ANSWER
1. Let X denote the amount of time for which a book on 2-hour reserve at a college-library is checked out by a
randomly selected student and suppose that X
Calculate the following probabilities:
a.
b.
ANS:
a.
b.
PTS: 1
2. A college professor always finishes his lectures within 2 minutes after the bell rings to end the period and the end of
the lecture. Let X = the time that elapses between the bell and the end of the lecture and suppose the pdf of X is
, a. Find the value of k. [Hint: Total area under the graph of f(x) is 1.]
b. What is the probability that the lecture ends within 1minutes of the bell ringing?
c. What is the probability that the lecture continues beyond the bell for between 60 and 90 seconds?
d. What is the probability that the lecture continues for at least 90 seconds beyond the bell?
ANS:
a.
b.
c.
d.
PTS: 1
3. The time X (minutes) for a lab assistant to prepare the equipment for a certain experiment is believed to have a
uniform distribution with A = 20 and B = 30.
a. Write the pdf of X and sketch its graph.
b. What is the probability that preparation time exceeds 27 minutes?
c. Find the preparation mean time, then calculate the probability that preparation is within 2 minutes of the mean
time?
d. For any a such that 20 < a < a + 2 < 30, what is the probability that preparation time is between a and a + 2
minutes?
ANS:
a.
b.
c.
25 2 is from 23 to 27 minutes:
d. since the interval has length 2.
PTS: 1
4. “Time headway” in traffic flow is the elapsed time between the time that one car finishes passing a fixed point and
the instant that the next car begins to pass that point. Let X = the time headway for two randomly chosen
consecutive cars on a freeway during a period of heavy flow. The following pdf of X is
, What is the probability that the time headway is
a. At most 6 seconds?
b. At least 6 seconds?
c. At most 5 seconds?
d. Between 5 and 6 seconds?
ANS:
a.
b.
c.
d.
PTS: 1
5. The cdf of checkout duration X for a book on a 2-hour reserve at a college library is given by:
Use this cdf to compute the following:
a.
b.
c.
d. The median checkout duration
e.
ANS:
a.
b.
c.
d.
