Finite Mathematics
7th Edition
ISBN: 9781337280426
Author: Stefan Waner, Steven Costenoble
Publisher: Cengage Learning
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Chapter 3.2, Problem 65E
To determine
The nature of solution of a homogenous system which has a unique solution.
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3. Prove that, for any random variable X, the minimum of E(X - a)² is attained
for a = EX.
Proved
Shade the areas given
7. Cantelli's inequality. Let X be a random variable with finite variance, o².
(a) Prove that, for x ≥ 0,
P(X EX2x)≤
02
x² +0²
202
P(|X - EX2x)<≤
(b) Find X assuming two values where there is equality.
(c) When is Cantelli's inequality better than Chebyshev's inequality?
(d) Use Cantelli's inequality to show that med (X) - EX ≤ o√√3; recall,
from Proposition 6.1, that an application of Chebyshev's inequality yields
the bound o√√2.
(e) Generalize Cantelli's inequality to moments of order r 1.
Chapter 3 Solutions
Finite Mathematics
Ch. 3.1 - In Exercises 1-6, find three different particular...Ch. 3.1 - In Exercises 1-6, find three different particular...Ch. 3.1 - In Exercises 1-6, find three different particular...Ch. 3.1 - In Exercises 1-6, find three different particular...Ch. 3.1 - In Exercises 1-6, find three different particular...Ch. 3.1 - Prob. 6ECh. 3.1 - Prob. 7ECh. 3.1 - Prob. 8ECh. 3.1 - In Exercises 7-20, find all solutions of the given...Ch. 3.1 - In Exercises 7-20, find all solutions of the given...
Ch. 3.1 - Prob. 11ECh. 3.1 - Prob. 12ECh. 3.1 - Prob. 13ECh. 3.1 - Prob. 14ECh. 3.1 - In Exercises 7-20, find all solutions of the given...Ch. 3.1 - In Exercises 7-20, find all solutions of the given...Ch. 3.1 - Prob. 17ECh. 3.1 - Prob. 18ECh. 3.1 - Prob. 19ECh. 3.1 - In Exercises 7-20, find all solutions of the given...Ch. 3.1 - In Exercises 21-30, use technol.ogy to obtain...Ch. 3.1 - Prob. 22ECh. 3.1 - Prob. 23ECh. 3.1 - Prob. 24ECh. 3.1 - In Exercises 21-30, use technol.ogy to obtain...Ch. 3.1 - Prob. 26ECh. 3.1 - Prob. 27ECh. 3.1 - Prob. 28ECh. 3.1 - Prob. 29ECh. 3.1 - In Exercises 21-30, use technol.ogy to obtain...Ch. 3.1 - In Exercises 31-38, translate the given statement...Ch. 3.1 - In Exercises 31-38, translate the given statement...Ch. 3.1 - In Exercises 31-38, translate the given statement...Ch. 3.1 - In Exercises 31-38, translate the given statement...Ch. 3.1 - In Exercises 31-38, translate the given statement...Ch. 3.1 - Prob. 36ECh. 3.1 - Prob. 37ECh. 3.1 - Prob. 38ECh. 3.1 - Prob. 39ECh. 3.1 - Class Scheduling Enormous State Universitys Math...Ch. 3.1 - Prob. 41ECh. 3.1 - Nutrition Anthony Altino is mixing food for his...Ch. 3.1 - Nutrition One serving of Campbell Soup Companys...Ch. 3.1 - Nutrition One serving of Campbell Soup Companys...Ch. 3.1 - Protein Supplements Exercises 45-48 are based on...Ch. 3.1 - Protein Supplements Exercises 45-48 are based on...Ch. 3.1 - Protein Supplements Exercises 45-48 are based on...Ch. 3.1 - Protein Supplements Exercises 45-48 are based on...Ch. 3.1 - Prob. 49ECh. 3.1 - Investments: Energy Stocks In the 3-rnonth period...Ch. 3.1 - Prob. 51ECh. 3.1 - Investments: High Dividend Stocks During the first...Ch. 3.1 - Voting An appropriations bill passed the U.S....Ch. 3.1 - Voting The U.S. Senate has 100 members. For a bill...Ch. 3.1 - Intramural Sports The best sports dorm on campus,...Ch. 3.1 - Law Five years ago, Enormous State Universitys...Ch. 3.1 - Purchasing (from the GMAT) Elena purchased Brand X...Ch. 3.1 - Purchasing (based on a question from the GMAT)...Ch. 3.1 - Prob. 59ECh. 3.1 - Equilibrium Price The demand and supply functions...Ch. 3.1 - Supply and Demand (from the GRE Economics Test)...Ch. 3.1 - Prob. 62ECh. 3.1 - Equilibrium Price In June 2001 the retail price of...Ch. 3.1 - Equilibrium Price At the start of December 2001...Ch. 3.1 - Pollution Joe Slo, a college sophomore, neglected...Ch. 3.1 - Prob. 66ECh. 3.1 - Prob. 67ECh. 3.1 - Prob. 68ECh. 3.1 - Prob. 69ECh. 3.1 - A system of three equations in two unknowns...Ch. 3.1 - Prob. 71ECh. 3.1 - Prob. 72ECh. 3.1 - Prob. 73ECh. 3.1 - Referring to Exercise 39, but using different...Ch. 3.1 - Prob. 75ECh. 3.1 - Prob. 76ECh. 3.1 - Select one: If the addition or subtraction of two...Ch. 3.1 - Select one: If adding two linear equations gives...Ch. 3.1 - Prob. 79ECh. 3.1 - Prob. 80ECh. 3.1 - How likely do you think it is that a random system...Ch. 3.1 - Prob. 82ECh. 3.2 - In Exercises 1-42, use Gauss-Jordan row reduction...Ch. 3.2 - In Exercises 1-42, use Gauss-Jordan row reduction...Ch. 3.2 - In Exercises 1-42, use Gauss-Jordan row reduction...Ch. 3.2 - In Exercises 1-42, use Gauss-Jordan row reduction...Ch. 3.2 - In Exercises 1-42, use Gauss-Jordan row reduction...Ch. 3.2 - Prob. 6ECh. 3.2 - Prob. 7ECh. 3.2 - Prob. 8ECh. 3.2 - In Exercises 1-42, use Gauss-Jordan row reduction...Ch. 3.2 - In Exercises 1-42, use Gauss-Jordan row reduction...Ch. 3.2 - Prob. 11ECh. 3.2 - Prob. 12ECh. 3.2 - In Exercises 1-42, use Gauss-Jordan row reduction...Ch. 3.2 - Prob. 14ECh. 3.2 - In Exercises 1-42, use Gauss-Jordan row reduction...Ch. 3.2 - In Exercises 1-42, use Gauss-Jordan row reduction...Ch. 3.2 - Prob. 17ECh. 3.2 - In Exercises 1-42, use Gauss-Jordan row reduction...Ch. 3.2 - Prob. 19ECh. 3.2 - In Exercises 1-42, use Gauss-Jordan row reduction...Ch. 3.2 - In Exercises 1-42, use Gauss-Jordan row reduction...Ch. 3.2 - In Exercises 1-42, use Gauss-Jordan row reduction...Ch. 3.2 - In Exercises 1-42, use Gauss-Jordan row reduction...Ch. 3.2 - In Exercises 1-42, use Gauss-Jordan row reduction...Ch. 3.2 - In Exercises 1-42, use Gauss-Jordan row reduction...Ch. 3.2 - Prob. 26ECh. 3.2 - Prob. 27ECh. 3.2 - Prob. 28ECh. 3.2 - In Exercises 1-42, use Gauss-Jordan row reduction...Ch. 3.2 - In Exercises 1-42, use Gauss-Jordan row reduction...Ch. 3.2 - Prob. 31ECh. 3.2 - Prob. 32ECh. 3.2 - Prob. 33ECh. 3.2 - Prob. 34ECh. 3.2 - In Exercises 1-42, use Gauss-Jordan row reduction...Ch. 3.2 - Prob. 36ECh. 3.2 - In Exercises 1-42, use Gauss-Jordan row reduction...Ch. 3.2 - Prob. 38ECh. 3.2 - Prob. 39ECh. 3.2 - In Exercises 1-42, use Gauss-Jordan row reduction...Ch. 3.2 - Prob. 41ECh. 3.2 - Prob. 42ECh. 3.2 - Prob. 43ECh. 3.2 - Prob. 44ECh. 3.2 - In Exercises 43-46, use technology to solve the...Ch. 3.2 - Prob. 46ECh. 3.2 - In Exercises 47-50, use technology to solve the...Ch. 3.2 - Prob. 48ECh. 3.2 - Prob. 49ECh. 3.2 - In Exercises 47-50, use technology to solve the...Ch. 3.2 - Prob. 51ECh. 3.2 - Prob. 52ECh. 3.2 - Prob. 53ECh. 3.2 - Prob. 54ECh. 3.2 - Prob. 55ECh. 3.2 - Prob. 56ECh. 3.2 - Your friend Frans tells you that the system of...Ch. 3.2 - Prob. 58ECh. 3.2 - Prob. 59ECh. 3.2 - Prob. 60ECh. 3.2 - Prob. 61ECh. 3.2 - Prob. 62ECh. 3.2 - Prob. 63ECh. 3.2 - Prob. 64ECh. 3.2 - Prob. 65ECh. 3.2 - Prob. 66ECh. 3.2 - Prob. 67ECh. 3.2 - Prob. 68ECh. 3.3 - Resource Allocation You manage an ice cream...Ch. 3.3 - Resource Allocation You own a hamburger franchise...Ch. 3.3 - Resource Allocation Urban Community College is...Ch. 3.3 - Resource Allocation The Enormous State University...Ch. 3.3 - Latin Music Sales (Digital) In 2013, total...Ch. 3.3 - Latin Music Sales (Digital) In 2012, total...Ch. 3.3 - Purchasing Aircraft In Example 2 we saw that...Ch. 3.3 - Purchasing Aircraft Refer to Exercise 7. Rene...Ch. 3.3 - Supply A bagel store orders cream cheese from...Ch. 3.3 - Supply Refer to Exercise 9. The bagel store's...Ch. 3.3 - Pest Control Halmar the Great has boasted to his...Ch. 3.3 - Manufacturing Perfume The Fancy French Perfume...Ch. 3.3 - Donations The Enormous State University Good Works...Ch. 3.3 - Tenure Professor Walt is up for tenure and wishes...Ch. 3.3 - Airline Costs Exercises 15and16 are based on the...Ch. 3.3 - Airline Costs Exercises 15and16 are based on the...Ch. 3.3 - Investing: Inverse Mutual Funds Inverse mutual...Ch. 3.3 - Investing: Inverse Mutual Funds Inverse mutual...Ch. 3.3 - Investing: Lesser-Known Stocks Exercises 19 and 20...Ch. 3.3 - Investing: Lesser-Known Stocks Exercises 19 and 20...Ch. 3.3 - Prob. 21ECh. 3.3 - Prob. 22ECh. 3.3 - Market Share: Homeowners Insurance Three market...Ch. 3.3 - Prob. 24ECh. 3.3 - Inventory Control Red Bookstore wants to ship...Ch. 3.3 - Inventory Control The Tubular Ride Boogie Board...Ch. 3.3 - Prob. 27ECh. 3.3 - Tourism in the 1990s In the 1990s, significant...Ch. 3.3 - Prob. 29ECh. 3.3 - Tobacco The following table shows some data from...Ch. 3.3 - Traffic Flow One-way traffic through Enormous...Ch. 3.3 - Traffic Flow The traffic through downtown East...Ch. 3.3 - Traffic Flow The traffic through downtown...Ch. 3.3 - Traffic Flow Officials of the town of Hempstead...Ch. 3.3 - Traffic Management The Outer Village Town Council...Ch. 3.3 - Electric Current Electric current measures (in...Ch. 3.3 - Econometrics (from the GRE Economics Test) This...Ch. 3.3 - Prob. 38ECh. 3.3 - CAT Scans CAT (computerized axial tomographic)...Ch. 3.3 - CAT Scans CAT (computerized axial tomographic)...Ch. 3.3 - Prob. 41ECh. 3.3 - Prob. 42ECh. 3.3 - Prob. 43ECh. 3.3 - Prob. 44ECh. 3.3 - Voting In the 75th Congress (1937-1939) the U.S....Ch. 3.3 - Prob. 46ECh. 3.3 - Investments Things have not been going too well...Ch. 3.3 - Prob. 48ECh. 3.3 - Prob. 49ECh. 3.3 - Suppose that you obtained a solution for Exercise...Ch. 3.3 - Prob. 51ECh. 3.3 - Prob. 52ECh. 3.3 - Prob. 53ECh. 3.3 - Prob. 54ECh. 3.3 - In Exercises 51-56, x, y and z represent the...Ch. 3.3 - In Exercises 51-56, x, y and z represent the...Ch. 3.3 - Make up an entertaining word problem leading to...Ch. 3.3 - Prob. 58ECh. 3 - In Exercises 16, graph the given equations and...Ch. 3 - Prob. 2RECh. 3 - Prob. 3RECh. 3 - In Exercises 16, graph the given equations and...Ch. 3 - Prob. 5RECh. 3 - Prob. 6RECh. 3 - In Exercises 718, solve the given system of linear...Ch. 3 - In Exercises 718, solve the given system of linear...Ch. 3 - In Exercises 718, solve the given system of linear...Ch. 3 - In Exercises 718, solve the given system of linear...Ch. 3 - Prob. 11RECh. 3 - Prob. 12RECh. 3 - In Exercises 718, solve the given system of linear...Ch. 3 - In Exercises 718, solve the given system of linear...Ch. 3 - Prob. 15RECh. 3 - In Exercises 718, solve the given system of linear...Ch. 3 - Prob. 17RECh. 3 - Prob. 18RECh. 3 - Exercises 1922 are based on the following equation...Ch. 3 - Prob. 20RECh. 3 - Prob. 21RECh. 3 - Prob. 22RECh. 3 - Prob. 23RECh. 3 - Prob. 24RECh. 3 - Prob. 25RECh. 3 - Prob. 26RECh. 3 - Prob. 27RECh. 3 - Prob. 28RECh. 3 - Prob. 29RECh. 3 - Prob. 30RECh. 3 - Prob. 31RECh. 3 - Purchasing You are the buyer for OHaganBooks.com...Ch. 3 - Prob. 33RECh. 3 - Prob. 34RECh. 3 - Feeding Schedules Billy-Sean OHagan is John...Ch. 3 - Prob. 36RECh. 3 - Website Traffic OHaganBooks.com has two principal...Ch. 3 - Sales As the buyer at OHaganBooks.com, you are...Ch. 3 - Investing in Stocks Billy-Sean OHagan is the...Ch. 3 - Prob. 40RECh. 3 - Prob. 41RECh. 3 - Prob. 42RECh. 3 - Prob. 43RECh. 3 - Prob. 44RECh. 3 - Prob. 45RECh. 3 - Prob. 46RE
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