/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q10E The number of pumps in use at bo... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Q10E (page 99)

The number of pumps in use at both a six-pump station and a four-pump station will be determined. Give the possible values for each of the following random variables:

a. T = the total number of pumps in use.

b. X = the difference between the numbers in use atstations 1 and 2.

c. U = the maximum number of pumps in use at either Station.

d. Z = the number of stations having exactly two pumps in use.

Short Answer

Expert verified

a. The possible values are\(T = \left\{ {0,1,2,3,4,5,6,7,8,9,10} \right\}\)

b. The possible values are\(X = \left\{ { - 4, - 3, - 2, - 1,0,1,2,3,4,5,6} \right\}\)

c. The possible values are\(U = \left\{ {0,1,2,3,4,5,6} \right\}\)

d. The possible values are\(Z = \left\{ {0,1,2} \right\}\)

Step by step solution

01

Given information

The data are provided that consists of both six-pump station and four-pump station.

02

Determine the possible values of random variable T

a.

ConsiderTto be total number of pumps in use out of two pump stations. One pump station consists of 6 pump stations while the other contains 4 stations.

In total, there are 10 pump stations. So, the minimum value of random variable is 0 and maximum is 10.

Then, Tcan be defined by:

\(T = \left\{ {0,1,2,3,4,5,6,7,8,9,10} \right\}\)

03

Determine the possible values of random variable X

b.

ConsiderXto bethe difference between the used pumps in two stations.

In this case, obtain the different combinations between the two-pump stations by accompanying table.

0

1

2

3

4

5

6

0

\[0--0 = 0\]

\[1--0 = 1\]

\[2--0 = 2\]

\[3--0 = 3\]

\[4--0 = 4\]

\[5--0 = 5\]

\[6--0 = 6\]

1

\[0--1 = - 1\]

\[1--1 = 0\]

\[2--1 = 1\]

\[3--1 = 2\]

\[4--1 = 3\]

\[5--1 = 4\]

\[6--1 = 5\]

2

\[0--2 = - 2\]

\[1--2 = - 1\]

\[2--2 = 0\]

\[3--2 = 1\]

\[4--2 = 2\]

\[5--2 = 3\]

\[6--2 = 4\]

3

\[0--3 = - 3\]

\[1--3 = - 2\]

\[2--3 = - 1\]

\[3--3 = 0\]

\[4--3 = 1\]

\[5--3 = 2\]

\[6--3 = 3\]

4

\[0--4 = - 4\]

\[1--4 = - 3\]

\(2 - 4 = - 2\)

\[3--4 = - 1\]

\[4--4 = 0\]

\[5--4 = 1\]

\[6--4 = 2\]

The extreme points are -4 and 6. Then, X can be defined by:

\(X = \left\{ { - 4, - 3, - 2, - 1,0,1,2,3,4,5,6} \right\}\)

04

Determine the possible values of random variable U

c.

Consider U to be the maximum number of pumps in use in either of the two stations.

In this case, obtain the different combinations between the two-pump stations by accompanying table.

0

1

2

3

0

\[\max \left( {0,0} \right) = 0\]

\[\max \left( {1,0} \right) = 1\]

\[\max \left( {2,0} \right) = 2\]

\[\max \left( {3,0} \right) = 3\]

1

\[\max \left( {0,1} \right) = 1\]

\[\max \left( {1,1} \right) = 1\]

\[\max \left( {2,1} \right) = 2\]

\[\max \left( {3,1} \right) = 3\]

2

\[\max \left( {0,2} \right) = 2\]

\[\max \left( {1,2} \right) = 2\]

\[\max \left( {2,2} \right) = 2\]

\[\max \left( {3,2} \right) = 3\]

3

\[\max \left( {0,3} \right) = 3\]

\[\max \left( {1,3} \right) = 3\]

\[\max \left( {2,3} \right) = 3\]

\[\max \left( {3,3} \right) = 3\]

4

\[\max \left( {0,4} \right) = 4\]

\[\max \left( {1,4} \right) = 4\]

\[\max \left( {2,4} \right) = 4\]

\[\max \left( {3,4} \right) = 4\]

4

5

6

0

\[\max \left( {4,0} \right) = 4\]

\[\max \left( {5,0} \right) = 5\]

\[\max \left( {6,0} \right) = 6\]

1

\[\max \left( {4,1} \right) = 4\]

\[\max \left( {5,1} \right) = 5\]

\[\max \left( {6,1} \right) = 6\]

2

\[\max \left( {4,2} \right) = 4\]

\[\max \left( {5,2} \right) = 5\]

\[\max \left( {6,2} \right) = 6\]

3

\[\max \left( {4,3} \right) = 4\]

\[\max \left( {5,3} \right) = 5\]

\[\max \left( {6,3} \right) = 6\]

4

\[\max \left( {4,4} \right) = 4\]

\[\max \left( {5,4} \right) = 5\]

\[\max \left( {6,4} \right) = 6\]

The extreme points are 0 and 6. Then, Ucan be defined by:

\(U = \left\{ {0,1,2,3,4,5,6} \right\}\)

05

Determine the possible values of random variable Z

d.

ConsiderZto be the number of stations having exactly two pumps in use in two stations.

In this case, obtain the different combinations between the two-pump stations by accompanying table.

0

1

2

3

4

5

6

0

\[\left( {0 + 0} \right) = 0\]

\[\left( {1 + 0} \right) = 1\]

\[\left( {2 + 0} \right) = 2\]

\[\left( {3 + 0} \right) = 3\]

\[\left( {4 + 0} \right) = 4\]

\[\left( {5 + 0} \right) = 5\]

\[\left( {6 + 0} \right) = 6\]

1

\[\left( {0 + 1} \right) = 1\]

\[\left( {1 + 1} \right) = 2\]

\[\left( {2 + 1} \right) = 3\]

\[\left( {3 + 1} \right) = 4\]

\[\left( {4 + 1} \right) = 5\]

\[\left( {5 + 1} \right) = 6\]

\[\left( {6 + 1} \right) = 7\]

2

\[\left( {0 + 2} \right) = 2\]

\[\left( {1 + 2} \right) = 3\]

\[\left( {2 + 2} \right) = 4\]

\[\left( {3 + 2} \right) = 5\]

\[\left( {4 + 2} \right) = 6\]

\[\left( {5 + 2} \right) = 7\]

\[\left( {6 + 2} \right) = 8\]

3

\[\left( {0 + 3} \right) = 3\]

\[\left( {1 + 3} \right) = 4\]

\[\left( {2 + 3} \right) = 5\]

\[\left( {3 + 3} \right) = 6\]

\[\left( {4 + 3} \right) = 7\]

\[\left( {5 + 3} \right) = 8\]

\[\left( {6 + 3} \right) = 9\]

4

\[\left( {0 + 4} \right) = 4\]

\[\left( {1 + 4} \right) = 5\]

\[\left( {2 + 4} \right) = 6\]

\[\left( {3 + 4} \right) = 7\]

\[\left( {4 + 4} \right) = 8\]

\[\left( {5 + 4} \right) = 9\]

\[\left( {6 + 0} \right) = 6\]

The minimum and maximum numbers are 0 and 10 respectively.

Then,\(Z\)can be defined by:

\(Z = \left\{ {0,1,2,3,4,6,7,8,9,10} \right\}\)

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Some parts of California are particularly earthquake prone. Suppose that in one metropolitan area, 25% of all homeowners are insured against earthquake damage. Four homeowners are to be selected at random; let X

denote the number among the four who have earthquake insurance.

a. Find the probability distribution of X. (Hint: Let S denote a homeowner who has insurance and F one who does not. Then one possible outcome is SFSS,

with probability (.25)(.75)(.25)(.25) and associated X value 3. There are 15 other outcomes.)

b. Draw the corresponding probability histogram.

c. What is the most likely value for X?

d. What is the probability that at least two of the four selected have earthquake insurance?

A second-stage smog alert has been called in a certain area of Los Angeles County in which there are \({\rm{50}}\) industrial firms. An inspector will visit \({\rm{10}}\) randomly selected firms to check for violations of regulations. a. If \({\rm{15}}\) of the firms are actually violating at least one regulation, what is the pmf of the number of firms visited by the inspector that are in violation of at least one regulation? b. If there are \({\rm{500}}\) firms in the area, of which \({\rm{150}}\) are in violation, approximate the pmf of part (a) by a simpler pmf. c. For X = the number among the 10 visited that are in violation, compute E(X) and V(X) both for the exact pmf and the approximating pmf in part (b).

Suppose small aircraft arrive at a certain airport according to a Poisson process with rate\(\alpha = 8\)per hour, so that the number of arrivals during a time period of t hours is a Poisson rv with parameter\(\mu = 8t\). a. What is the probability that exactly 6 small aircraft arrive during a one-hour period? At least\(6\)? At least\({\bf{10}}\)? b. What are the expected value and standard deviations of the number of small aircraft that arrive during a\({\bf{90}}\)-min period? c. What is the probability that at least\({\bf{20}}\)small aircraft arrive during a\({\bf{2}}.{\bf{5}}\)-hour period? That at most\({\bf{10}}\)arrive during this period?

An individual named Claudius is located at the point 0 in the accompanying diagram. Using an appropriate randomization device (such as a
tetrahedral die, one having four sides), Claudius first moves to one of the four locations B1, B2, B3, B4. Once at one of these locations, another randomization device is used to decide whether Claudius next returns to 0 or next visits one of the other two adjacent points. This process then continues; after each move, another move to one of the (new) adjacent points is determined by tossing an appropriate die or coin.

a. Let X = the number of moves that Claudius makes before first returning to 0. What are possible values of X? Is X discrete or continuous?

b. If moves are allowed also along the diagonal paths connecting 0 to A1, A2, A3, and A4, respectively, answer the questions in part (a).

A personnel director interviewing \({\rm{11}}\) senior engineers for four job openings has scheduled six interviews for the first day and five for the second day of interviewing. Assume that the candidates are interviewed in random order. a. What is the probability that x of the top four candidates are interviewed on the first day? b. How many of the top four candidates can be expected to be interviewed on the first day?
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

Calculus

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.