Solution Found!
Solved: Consider the pdf for total waiting time Y for two
Chapter 4, Problem 20E(choose chapter or problem)
Problem 20E
Consider the pdf for total waiting time Y for two buses
introduced in Exercise 8.
a. Compute and sketch the cdf of Y. [Hint: Consider separately 0≤y<5 and 5≤y≤10 in computing F(y). A graph of the pdf should be helpful.]
b. Obtain an expression for the (100p)th percentile. [Hint: Consider separately 0
c. Compute E(Y ) and V(Y). How do these compare with the expected waiting time and variance for a single bus when the time is uniformly distributed on [0, 5]?
Reference exercise 8
In commuting to work, a professor must first get on a bus near her house and then transfer to a second bus. If the waiting time (in minutes) at each stop has a uniform distribution with A = 0 and B = 5 , then it can be shown that the total waiting time Y has the pdf
a. Sketch a graph of the pdf of Y.
b. Verify that .
c. What is the probability that total waiting time is at most 3 min?
d. What is the probability that total waiting time is at most 8 min?
e. What is the probability that total waiting time is between 3 and 8 min?
f. What is the probability that total waiting time is either less than 2 min or more than 6 min?
Questions & Answers
QUESTION:
Problem 20E
Consider the pdf for total waiting time Y for two buses
introduced in Exercise 8.
a. Compute and sketch the cdf of Y. [Hint: Consider separately 0≤y<5 and 5≤y≤10 in computing F(y). A graph of the pdf should be helpful.]
b. Obtain an expression for the (100p)th percentile. [Hint: Consider separately 0
c. Compute E(Y ) and V(Y). How do these compare with the expected waiting time and variance for a single bus when the time is uniformly distributed on [0, 5]?
Reference exercise 8
In commuting to work, a professor must first get on a bus near her house and then transfer to a second bus. If the waiting time (in minutes) at each stop has a uniform distribution with A = 0 and B = 5 , then it can be shown that the total waiting time Y has the pdf
a. Sketch a graph of the pdf of Y.
b. Verify that .
c. What is the probability that total waiting time is at most 3 min?
d. What is the probability that total waiting time is at most 8 min?
e. What is the probability that total waiting time is between 3 and 8 min?
f. What is the probability that total waiting time is either less than 2 min or more than 6 min?
ANSWER:
Answer
Step 1 of 3
a)For 0y<5
f(y)=y dy=
=y2