Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 3.4, Problem 64E
Show that E(X) = np when X is a binomial random variable. [Hint: First express E(X) as a sum with lower limit x = 1. Then factor out np, let y = x − 1 so that the sum is from y = 0 to y = n − 1, and show that the sum equals 1.]
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
The average number of minutes Americans commute to work is 27.7 minutes (Sterling's Best Places, April 13, 2012). The average commute time in minutes for 48 cities are as follows:
Click on the datafile logo to reference the data.
DATA file
Albuquerque
23.3
Jacksonville
26.2
Phoenix
28.3
Atlanta
28.3
Kansas City
23.4
Pittsburgh
25.0
Austin
24.6
Las Vegas
28.4
Portland
26.4
Baltimore
32.1
Little Rock
20.1
Providence
23.6
Boston
31.7
Los Angeles
32.2
Richmond
23.4
Charlotte
25.8
Louisville
21.4
Sacramento
25.8
Chicago
38.1
Memphis
23.8
Salt Lake City
20.2
Cincinnati
24.9
Miami
30.7
San Antonio
26.1
Cleveland
26.8
Milwaukee
24.8
San Diego
24.8
Columbus
23.4
Minneapolis
23.6
San Francisco
32.6
Dallas
28.5
Nashville
25.3
San Jose
28.5
Denver
28.1
New Orleans
31.7
Seattle
27.3
Detroit
29.3
New York
43.8
St. Louis
26.8
El Paso
24.4
Oklahoma City
22.0
Tucson
24.0
Fresno
23.0
Orlando
27.1
Tulsa
20.1
Indianapolis
24.8
Philadelphia
34.2
Washington, D.C.
32.8
a. What is the mean commute time for…
Morningstar tracks the total return for a large number of mutual funds. The following table shows the total return and the number of funds for four categories of mutual funds.
Click on the datafile logo to reference the data.
DATA file
Type of Fund
Domestic Equity
Number of Funds
Total Return (%)
9191
4.65
International Equity
2621
18.15
Hybrid
1419
2900
11.36
6.75
Specialty Stock
a. Using the number of funds as weights, compute the weighted average total return for these mutual funds. (to 2 decimals)
%
b. Is there any difficulty associated with using the "number of funds" as the weights in computing the weighted average total return in part (a)? Discuss. What else might be used for weights?
The input in the box below will not be graded, but may be reviewed and considered by your instructor.
c. Suppose you invested $10,000 in this group of mutual funds and diversified the investment by placing $2000 in Domestic Equity funds, $4000 in International Equity funds, $3000 in Specialty Stock…
The days to maturity for a sample of five money market funds are shown here. The dollar amounts invested in the funds are provided.
Days to
Maturity
20
Dollar Value
($ millions)
20
12
30
7
10
5
6
15
10
Use the weighted mean to determine the mean number of days to maturity for dollars invested in these five money market funds (to 1 decimal).
days
Chapter 3 Solutions
Probability and Statistics for Engineering and the Sciences
Ch. 3.1 - A concrete beam may fail either by shear (S) or...Ch. 3.1 - Using the experiment in Example 3.3, define two...Ch. 3.1 - Let X = the number of nonzero digits in a randomly...Ch. 3.1 - If the sample space S is an infinite set, does...Ch. 3.1 - Starting at a fixed time, each car entering an...Ch. 3.1 - For each random variable defined here, describe...Ch. 3.1 - Each time a component is tested, the trial is a...Ch. 3.1 - An individual named Claudius is located at the...Ch. 3.1 - The number of pumps in use at both a six-pump...Ch. 3.2 - Let X be the number of students who show up for a...
Ch. 3.2 - Airlines sometimes overbook flights. Suppose that...Ch. 3.2 - A mail-order computer business has six telephone...Ch. 3.2 - A contractor is required by a county planning...Ch. 3.2 - Many manufacturers have quality control programs...Ch. 3.2 - Some parts of California are particularly...Ch. 3.2 - A now batterys voltage may be acceptable (A) or...Ch. 3.2 - Two fair six-sided dice are tossed independently....Ch. 3.2 - A library subscribes to two different weekly news...Ch. 3.2 - Three couples and two single individuals have been...Ch. 3.2 - Suppose that you read through this years issues of...Ch. 3.2 - Refer to Exercise 13, and calculate and graph the...Ch. 3.2 - A branch of a certain bank in New York City has...Ch. 3.2 - An insurance company offers its policyholders a...Ch. 3.2 - In Example 3.12, let Y = the number of girls born...Ch. 3.2 - Alvie Singer lives at 0 in the accompanying...Ch. 3.2 - After all students have left the classroom, a...Ch. 3.2 - Show that the cdf F(x) is a nondecreasing...Ch. 3.3 - The pmf of the amount of memory X(GB) in a...Ch. 3.3 - An individual who has automobile insurance from a...Ch. 3.3 - Refer to Exercise 12 and calculate V(Y) and Y....Ch. 3.3 - A certain brand of upright freezer is available in...Ch. 3.3 - Let X be a Bernoulli rv with pmf as in Example...Ch. 3.3 - Suppose that the number of plants of a particular...Ch. 3.3 - A small market orders copies of a certain magazine...Ch. 3.3 - Let X be the damage incurred (in ) in a certain...Ch. 3.3 - The n candidates for a job have been ranked 1, 2,...Ch. 3.3 - Possible values of X, the number of components in...Ch. 3.3 - A chemical supply company currently has in stock...Ch. 3.3 - a. Draw a line graph of the pmf of X in Exercise...Ch. 3.3 - Use the definition in Expression (3.13) to prove...Ch. 3.3 - Suppose E(X) = 5 and E[X(X - 1)] = 27.5. What is...Ch. 3.3 - Write a general rule for E(X c) where c is a...Ch. 3.3 - A result called Chebyshevs inequality states that...Ch. 3.3 - If a X b, show that a E(X) b.Ch. 3.4 - Compute the following binomial probabilities...Ch. 3.4 - The article Should You Report That Fender-Bender?...Ch. 3.4 - NBC News reported on May 2. 2013. that 1 in 20...Ch. 3.4 - A company that produces fine crystal knows from...Ch. 3.4 - A particular telephone number is used to receive...Ch. 3.4 - Refer to the previous exercise. a. What is the...Ch. 3.4 - Suppose that 30% of all students who have to buy a...Ch. 3.4 - Exercise 30 (Section 3.3) gave the pmf of Y, the...Ch. 3.4 - A particular type of tennis racket comes in a...Ch. 3.4 - Twenty percent of all telephones of a certain type...Ch. 3.4 - The College Board reports that 2% of the 2 million...Ch. 3.4 - A certain type of flashlight requires two type-D...Ch. 3.4 - A very large batch of components has arrived at a...Ch. 3.4 - An ordinance requiring that a smoke detector be...Ch. 3.4 - A toll bridge charges 1.00 for passenger cars and...Ch. 3.4 - A student who is trying to write a paper for a...Ch. 3.4 - a. For fixed n, are there values of p(0 p 1) for...Ch. 3.4 - a. Show that b(x; n, 1 p) = b(n x; n, p). b....Ch. 3.4 - Show that E(X) = np when X is a binomial random...Ch. 3.4 - Customers at a gas station pay with a credit card...Ch. 3.4 - An airport limousine can accommodate up to four...Ch. 3.4 - Refer to Chebyshevs inequality given in Exercise...Ch. 3.5 - Eighteen individuals are scheduled to take a...Ch. 3.5 - Each of 12 refrigerators of a certain type has...Ch. 3.5 - An instructor who taught two sections of...Ch. 3.5 - A geologist has collected 10 specimens of basaltic...Ch. 3.5 - A personnel director interviewing 11 senior...Ch. 3.5 - Twenty pairs of individuals playing in a bridge...Ch. 3.5 - A second-stage smog alert has been called in a...Ch. 3.5 - The probability that a randomly selected box of a...Ch. 3.5 - A family decides to have children until it has...Ch. 3.5 - Three brothers and their wives decide to have...Ch. 3.5 - According to the article Characterizing the...Ch. 3.6 - The article Expectation Analysis of the...Ch. 3.6 - Let X be the number of material anomalies...Ch. 3.6 - Suppose that the number of drivers who travel...Ch. 3.6 - Consider writing onto a computer disk and then...Ch. 3.6 - An article in the Los Angeles Times (Dec. 3. 1993)...Ch. 3.6 - The Centers for Disease Control and Prevention...Ch. 3.6 - Suppose small aircraft arrive at a certain airport...Ch. 3.6 - Organisms are present in ballast water discharged...Ch. 3.6 - The number of requests for assistance received by...Ch. 3.6 - In proof testing of circuit boards, the...Ch. 3.6 - The article Reliability-Based Service-Life...Ch. 3.6 - Let X have a Poisson distribution with parameter ....Ch. 3.6 - Suppose that trees are distributed in a forest...Ch. 3.6 - Automobiles arrive at a vehicle equipment...Ch. 3.6 - a. In a Poisson process, what has to happen in...Ch. 3 - Consider a deck consisting of seven cards, marked...Ch. 3 - After shuffling a deck of 52 cards, a dealer deals...Ch. 3 - The negative binomial rv X was defined as the...Ch. 3 - Of all customers purchasing automatic garage-door...Ch. 3 - In some applications the distribution of a...Ch. 3 - A k-out-of-n system is one that will function if...Ch. 3 - A manufacturer of integrated circuit chips wishes...Ch. 3 - Of the people passing through an airport metal...Ch. 3 - An educational consulting firm is trying to decide...Ch. 3 - Consider a disease whose presence can be...Ch. 3 - Let p1 denote the probability that any particular...Ch. 3 - The purchaser of a power-generating unit requires...Ch. 3 - A plan for an executive travelers club has been...Ch. 3 - Forty percent of seeds from maize (modern-day com)...Ch. 3 - A trial has just resulted in a hung jury because...Ch. 3 - A reservation service employs five information...Ch. 3 - Grasshoppers arc distributed at random in a large...Ch. 3 - A newsstand has ordered five copies of a certain...Ch. 3 - Individuals A and B begin to play a sequence of...Ch. 3 - A test for the presence of a certain disease has...Ch. 3 - Prob. 114SECh. 3 - There are two Certified Public Accountants in a...Ch. 3 - The mode of a discrete random variable X with pmf...Ch. 3 - A computer disk storage device has ten concentric...Ch. 3 - If X is a hypergeometric rv, show directly from...Ch. 3 - Prob. 119SECh. 3 - Prob. 120SECh. 3 - Prob. 121SECh. 3 - Prob. 122SE
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Similar questions
- c. What are the first and third quartiles? First Quartiles (to 1 decimals) Third Quartiles (to 4 decimals) × ☑ Which companies spend the most money on advertising? Business Insider maintains a list of the top-spending companies. In 2014, Procter & Gamble spent more than any other company, a whopping $5 billion. In second place was Comcast, which spent $3.08 billion (Business Insider website, December 2014). The top 12 companies and the amount each spent on advertising in billions of dollars are as follows. Click on the datafile logo to reference the data. DATA file Company Procter & Gamble Comcast Advertising ($billions) $5.00 3.08 2.91 Company American Express General Motors Advertising ($billions) $2.19 2.15 ETET AT&T Ford Verizon L'Oreal 2.56 2.44 2.34 Toyota Fiat Chrysler Walt Disney Company J.P Morgan a. What is the mean amount spent on advertising? (to 2 decimals) 2.55 b. What is the median amount spent on advertising? (to 3 decimals) 2.09 1.97 1.96 1.88arrow_forwardMartinez Auto Supplies has retail stores located in eight cities in California. The price they charge for a particular product in each city are vary because of differing competitive conditions. For instance, the price they charge for a case of a popular brand of motor oil in each city follows. Also shown are the number of cases that Martinez Auto sold last quarter in each city. City Price ($) Sales (cases) Bakersfield 34.99 501 Los Angeles 38.99 1425 Modesto 36.00 294 Oakland 33.59 882 Sacramento 40.99 715 San Diego 38.59 1088 San Francisco 39.59 1644 San Jose 37.99 819 Compute the average sales price per case for this product during the last quarter? Round your answer to two decimal places.arrow_forwardConsider the following data and corresponding weights. xi Weight(wi) 3.2 6 2.0 3 2.5 2 5.0 8 a. Compute the weighted mean (to 2 decimals). b. Compute the sample mean of the four data values without weighting. Note the difference in the results provided by the two computations (to 3 decimals).arrow_forward
- Expert only,if you don't know it don't attempt it, no Artificial intelligence or screen shot it solvingarrow_forwardFor context, the image provided below is a quesion from a Sepetember, 2024 past paper in statistical modelingarrow_forwardFor context, the images attached below (the question and the related figure) is from a january 2024 past paperarrow_forward
- For context, the image attached below is a question from a June 2024 past paper in statisical modelingarrow_forwardFor context, the images attached below are a question from a June, 2024 past paper in statistical modelingarrow_forwardFor context, the images attached below (question and related graph) are from a February 2024 past paper in statistical modelingarrow_forward
- For context, the images attached below are from a February 2024 past paper in statistical modelingarrow_forwardFor context, the image provided below is a question from a September, 2024 past paper in statistical modelingarrow_forwardFor context, the image below is from a January 2024 past paper in statistical modelingarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Mod-01 Lec-01 Discrete probability distributions (Part 1); Author: nptelhrd;https://www.youtube.com/watch?v=6x1pL9Yov1k;License: Standard YouTube License, CC-BY
Discrete Probability Distributions; Author: Learn Something;https://www.youtube.com/watch?v=m9U4UelWLFs;License: Standard YouTube License, CC-BY
Probability Distribution Functions (PMF, PDF, CDF); Author: zedstatistics;https://www.youtube.com/watch?v=YXLVjCKVP7U;License: Standard YouTube License, CC-BY
Discrete Distributions: Binomial, Poisson and Hypergeometric | Statistics for Data Science; Author: Dr. Bharatendra Rai;https://www.youtube.com/watch?v=lHhyy4JMigg;License: Standard Youtube License