# Consider the pdf for total waiting time Y or two buses

## Problem 20E Chapter 4

Probability and Statistics for Engineering and the Sciences | 9th Edition

• 2901 Step-by-step solutions solved by professors and subject experts
• Get 24/7 help from StudySoup virtual teaching assistants

Probability and Statistics for Engineering and the Sciences | 9th Edition

4 5 0 299 Reviews
19
0
Problem 20E

Consider the pdf for total waiting time Y? ? or 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 (100?p?)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.?? ketch a graph of the pdf of ?Y?. b.?? erify that . c.?? hat is the probability that total waiting time is at most 3 min? d.?? hat is the probability that total waiting time is at most 8 min? e.?? hat 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?

Step-by-Step Solution:

Answer Step 1 of 3 a)For 0y<5 y 1 1 2 y f(y)= 25y dy= 50 [ ] 0 0 1 2 = 50y Step 2 of 6 For 5y<10 5 y f(y)= 1 y dy+ 2 - 1 y dy 25 5 25 0 5 2 y 1 y 2 5 2y y = 50 [ ] 0+ [ 5 50] 5 2y y2 = 5 - 50 -1 Step 3 of 6 The cdf of y is f(y)=0, y<0 1 2 = 50y , 0y<5 2y y2 = 5 - 50 -1, 5y<10 =1, y>0 Step 4 of 6 Step 5 of 6 b)The 100% percentile is 2y y 2 1= - -1 5 50 Rearrange the equation then we get y -20y+100=0 Solve for y We get y=10 Step 6 of 6 5 10 1 2 2 1 2 c)E(y)= yf(y)dy = 25y dy+ ( 5 y- 25 y )dy 0 5 1 3 5 2y 2 y3 10 = 75 [ ] 0+ [ 10 75] 5 =5 2 5 10 E(y )= y f(y)dy = 25 y dy+ ( 5 y -25y )dy 0 5 5 3 4 10 = 1 [ ]4 0 + [ 2y y ] 75 10 75 5 =29.167 V(y)=E(y )-E(y) 2 =29.167-25 =4.167 Problem 2 Reference exercise 8 Step 1 of 7 a) The probability distribution is x 0 1 2 3 4 5 6 7 8 9 10 f(x) 0 0.04 0.08 0.12 0.16 0.2 0.16 0.12 0.08 0.04 0 Step 2 of 7 Step 3 of 7 5 10 b) f(y)dy = 1 y dy+ ( 2- 1 y )dy 0 25 5 5 25 5 2 3 10 = 1 [ ]2 +[ y y ] 50 0 5 50 5 1 1 = 2((4-2)-(2- )2½+½=1 Step 4 of 7 c) The probability that total waiting time is at most 3 min =p(x3)=0+0.04+0.08+0.12=0.24

Step 5 of 7

Step 6 of 7

##### ISBN: 9780321629111

This textbook survival guide was created for the textbook: Probability and Statistics for Engineering and the Sciences, edition: 9. This full solution covers the following key subjects: Waiting, min, Probability, pdf, bus. This expansive textbook survival guide covers 18 chapters, and 1582 solutions. The answer to “Consider the pdf for total waiting time Y? ? or 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 (100?p?)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.?? ketch a graph of the pdf of ?Y?. b.?? erify that . c.?? hat is the probability that total waiting time is at most 3 min? d.?? hat is the probability that total waiting time is at most 8 min? e.?? hat 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?” is broken down into a number of easy to follow steps, and 220 words. Since the solution to 20E from 4 chapter was answered, more than 555 students have viewed the full step-by-step answer. Probability and Statistics for Engineering and the Sciences was written by and is associated to the ISBN: 9780321629111. The full step-by-step solution to problem: 20E from chapter: 4 was answered by , our top Statistics solution expert on 05/06/17, 06:21PM.

#### Related chapters

Unlock Textbook Solution

Enter your email below to unlock your verified solution to:

Consider the pdf for total waiting time Y or two buses

×
Get Full Access to Probability And Statistics For Engineering And The Sciences - 9 Edition - Chapter 4 - Problem 20e

Get Full Access to Probability And Statistics For Engineering And The Sciences - 9 Edition - Chapter 4 - Problem 20e

I don't want to reset my password

Need help? Contact support

Need an Account? Is not associated with an account
We're here to help

Having trouble accessing your account? Let us help you, contact support at +1(510) 944-1054 or support@studysoup.com

Password Reset Request Sent An email has been sent to the email address associated to your account. Follow the link in the email to reset your password. If you're having trouble finding our email please check your spam folder
Already have an Account? Is already in use