Introductory Statistics (10th Edition)
10th Edition
ISBN: 9780321989178
Author: Neil A. Weiss
Publisher: PEARSON
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Chapter 5.3, Problem 73E
To determine
The
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Pam, Rob and Sam get a cake that is one-third chocolate, one-third vanilla, and one-third strawberry as shown below. They wish to fairly divide the cake using the lone chooser method. Pam likes strawberry twice as much as chocolate or vanilla. Rob only likes chocolate. Sam, the chooser, likes vanilla and strawberry twice as much as chocolate. In the first division, Pam cuts the strawberry piece off and lets Rob choose his favorite piece. Based on that, Rob chooses the chocolate and vanilla parts. Note: All cuts made to the cake shown below are vertical.Which is a second division that Rob would make of his share of the cake?
Three players (one divider and two choosers) are going to divide a cake fairly using the lone divider method. The divider cuts the cake into three slices (s1, s2, and s3).
If the choosers' declarations are Chooser 1: {s1 , s2} and Chooser 2: {s2 , s3}.
Using the lone-divider method, how many different fair divisions of this cake are possible?
Theorem 2.6 (The Minkowski inequality)
Let p≥1. Suppose that X and Y are random variables, such that E|X|P <∞ and
E|Y P <00. Then
X+YpX+Yp
Chapter 5 Solutions
Introductory Statistics (10th Edition)
Ch. 5.1 - Fill in the blanks. a. A relative-frequency...Ch. 5.1 - Provide an example (other than one discussed in...Ch. 5.1 - Let X denote the number of siblings of a randomly...Ch. 5.1 - Fill in the blank. For a discrete random variable,...Ch. 5.1 - Suppose that you make a large number of...Ch. 5.1 - What rule of probability permits you to obtain any...Ch. 5.1 - A variable x of a finite population has the...Ch. 5.1 - A variable y of a finite population has the...Ch. 5.1 - A variable y of a finite population has the...Ch. 5.1 - A variable x of a finite population has the...
Ch. 5.1 - Space Shuttles. The National Aeronautics and Space...Ch. 5.1 - Persons per Housing Unit. From the document...Ch. 5.1 - Major Hurricanes. The Atlantic Hurricane Database...Ch. 5.1 - Childrens Gender. A certain couple is equally...Ch. 5.1 - Dice. When two balanced dice are rolled, 36...Ch. 5.1 - World Series. The World Series in baseball is won...Ch. 5.1 - Archery. An archer shoots an arrow into a square...Ch. 5.1 - Solar Eclipses. The World Almanac provides...Ch. 5.1 - Black Bear Litters. In the article Reproductive...Ch. 5.1 - All-Numeric Passwords. The technology consultancy...Ch. 5.1 - Suppose that P(Z 1.96) = 0.025. Find P(Z 1.96)....Ch. 5.1 - Suppose that T and Z are random variables. a. If...Ch. 5.1 - Prob. 23ECh. 5.2 - What concept does the mean of a discrete random...Ch. 5.2 - Comparing Investments. Suppose that the random...Ch. 5.2 - In Exercises 5.275.30, we have provided the...Ch. 5.2 - In Exercises 5.275.30, we have provided the...Ch. 5.2 - In Exercises 5.275.30, we have provided the...Ch. 5.2 - In Exercises 5.275.30, we have provided the...Ch. 5.2 - In Exercises 5.315.35, we have provided the...Ch. 5.2 - In Exercises 5.315.35, we have provided the...Ch. 5.2 - In Exercises 5.315.35, we have provided the...Ch. 5.2 - In Exercises 5.315.35, we have provided the...Ch. 5.2 - In Exercises 5.315.35, we have provided the...Ch. 5.2 - World Series. The World Series in baseball is won...Ch. 5.2 - Archery. An archer shoots an arrow into a square...Ch. 5.2 - All-Numeric Passwords. The technology consultancy...Ch. 5.2 - Expected Value. As noted in Definition 5.4 on page...Ch. 5.2 - Evaluating Investments. An investor plans to put...Ch. 5.2 - Homeowners Policy. An insurance company wants to...Ch. 5.2 - Prob. 42ECh. 5.2 - Equipment Breakdowns. A factory manager collected...Ch. 5.2 - Simulation. Let X be the value of a randomly...Ch. 5.2 - Mean as Center of Gravity. Let X be a discrete...Ch. 5.2 - Equipment Breakdowns. Refer to Exercise 5.43....Ch. 5.2 - Equipment Breakdowns. The factory manager in...Ch. 5.3 - In probability and statistics, what is each...Ch. 5.3 - Under what three conditions are repeated trials of...Ch. 5.3 - Explain the significance of binomial coefficients...Ch. 5.3 - Discuss the pros and cons of binomial probability...Ch. 5.3 - What is the binomial distribution?Ch. 5.3 - Suppose that a simple random sample is taken from...Ch. 5.3 - Give two examples of Bernoulli trials other than...Ch. 5.3 - What does the bi in binomial signify?Ch. 5.3 - Compute 3!, 7!, 8!, and 9!.Ch. 5.3 - Find 1!, 2!, 4!, and 6!.Ch. 5.3 - Evaluate the following binomial coefficients. a....Ch. 5.3 - Evaluate the following binomial coefficients. a....Ch. 5.3 - Evaluate the following binomial coefficients. a....Ch. 5.3 - Determine the value of each binomial coefficient....Ch. 5.3 - For each of the following probability histograms...Ch. 5.3 - For each of the following probability histograms...Ch. 5.3 - Pinworm Infestation. Pinworm infestation, which is...Ch. 5.3 - Psychiatric Disorders. The National Institute of...Ch. 5.3 - In each of Exercises 5.675.72, we have provided...Ch. 5.3 - In each of Exercises 5.675.72, we have provided...Ch. 5.3 - In each of Exercises 5.675.72, we have provided...Ch. 5.3 - In each of Exercises 5.675.72, we have provided...Ch. 5.3 - In each of Exercises 5.675.72, we have provided...Ch. 5.3 - In each of Exercises 5.675.72, we have provided...Ch. 5.3 - Prob. 73ECh. 5.3 - Psychiatric Disorders. Use Procedure 5.1 on page...Ch. 5.3 - Tossing a Coin. If we repeatedly toss a balanced...Ch. 5.3 - Rolling a Die. If we repeatedly roll a balanced...Ch. 5.3 - Horse Racing. According to the Daily Racing Form,...Ch. 5.3 - Gestation Periods. The probability is 0.314 that...Ch. 5.3 - Traffic Fatalities and Intoxication. The National...Ch. 5.3 - Multiple-Choice Exams. A student takes a...Ch. 5.3 - Love Stinks? J. Fetto, in the article Love Stinks...Ch. 5.3 - Carbon Tax. A poll commissioned by Friends of the...Ch. 5.3 - Video Games. A pathological video game user (PVGU)...Ch. 5.3 - Recidivism. In the Scientific American article...Ch. 5.3 - Roulette. A success, s, in Bernoulli trials is...Ch. 5.3 - Sampling and the Binomial Distribution. Refer to...Ch. 5.3 - Sampling and the Binomial Distribution. Following...Ch. 5.3 - The Hypergeometric Distribution. In this exercise,...Ch. 5.3 - To illustrate, again consider the Mega Millions...Ch. 5.3 - To illustrate, consider the following problem:...Ch. 5.4 - Identify two uses of Poisson distributions.Ch. 5.4 - Why cant all the probabilities for a Poisson...Ch. 5.4 - For a Poisson random variable, what is the...Ch. 5.4 - What conditions should be satisfied in order to...Ch. 5.4 - Prob. 95ECh. 5.4 - Prob. 96ECh. 5.4 - In each of Exercises 5.965.99, we have provided...Ch. 5.4 - Prob. 98ECh. 5.4 - In each of Exercises 5.965.99, we have provided...Ch. 5.4 - Amusement Ride Safety. Approximately 297 million...Ch. 5.4 - Polonium. In the 1910 article The Probability...Ch. 5.4 - Wasps. M. Goodisman et al. studied patterns in...Ch. 5.4 - Wars. In the paper The Distribution of Wars in...Ch. 5.4 - Motel Reservations. M. Driscoll and N. Weiss...Ch. 5.4 - Cherry Pies. At one time, a well-known restaurant...Ch. 5.4 - Motor-Vehicle Deaths. According to Injury Facts, a...Ch. 5.4 - Prisoners. From the U.S. Census Bureau and the...Ch. 5.4 - The Challenger Disaster. In a letter to the editor...Ch. 5.4 - Fragile X Syndrome. The second-leading genetic...Ch. 5.4 - Holes in One. Refer to the case study on page 223....Ch. 5.4 - A Yellow Lobster! As reported by the Associated...Ch. 5.4 - With regard to the use of a Poisson distribution...Ch. 5.4 - Roughly speaking, you can use the Poisson...Ch. 5 - Fill in the blanks. a. A ______ is a quantitative...Ch. 5 - Prob. 2RPCh. 5 - Prob. 3RPCh. 5 - If you sum the probabilities of the possible...Ch. 5 - A random variable X equals 2 with probability...Ch. 5 - A random variable X has mean 3.6. If you make a...Ch. 5 - Prob. 7RPCh. 5 - Prob. 8RPCh. 5 - Prob. 9RPCh. 5 - List the three requirements for repeated trials of...Ch. 5 - What is the relationship between Bernoulli trials...Ch. 5 - In 10 Bernoulli trials, how many outcomes contain...Ch. 5 - Craps. The game of craps is played by rolling two...Ch. 5 - Following are two probability histograms of...Ch. 5 - Prob. 15RPCh. 5 - Prob. 16RPCh. 5 - ASU Enrollment Summary. According to the Arizona...Ch. 5 - Prob. 18RPCh. 5 - Busy Phone Lines. Refer to the probability...Ch. 5 - Craps. Use the binomial probability formula to...Ch. 5 - Penalty Kicks. In the game of soccer, a penalty...Ch. 5 - Pets. According to JAVMA News, a publication of...Ch. 5 - Pets. Refer to Problem 22. a. Draw a probability...Ch. 5 - Prob. 24RPCh. 5 - Prob. 25RPCh. 5 - Meteoroids. In the article Interstellar Pelting...Ch. 5 - Emphysema. The respiratory disease emphysema,...Ch. 5 - Prob. 28RPCh. 5 - As we reported at the beginning of this chapter,...
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Similar questions
- Theorem 1.2 (1) Suppose that P(|X|≤b) = 1 for some b > 0, that EX = 0, and set Var X = 0². Then, for 0 0, P(X > x) ≤e-x+1²² P(|X|>x) ≤2e-1x+1²² (ii) Let X1, X2...., Xn be independent random variables with mean 0, suppose that P(X ≤b) = 1 for all k, and set oσ = Var X. Then, for x > 0. and 0x) ≤2 exp Σ k=1 (iii) If, in addition, X1, X2, X, are identically distributed, then P(S|x) ≤2 expl-tx+nt²o).arrow_forwardTheorem 5.1 (Jensen's inequality) state without proof the Jensen's Ineg. Let X be a random variable, g a convex function, and suppose that X and g(X) are integrable. Then g(EX) < Eg(X).arrow_forwardCan social media mistakes hurt your chances of finding a job? According to a survey of 1,000 hiring managers across many different industries, 76% claim that they use social media sites to research prospective candidates for any job. Calculate the probabilities of the following events. (Round your answers to three decimal places.) answer parts a-c. a) Out of 30 job listings, at least 19 will conduct social media screening. b) Out of 30 job listings, fewer than 17 will conduct social media screening. c) Out of 30 job listings, exactly between 19 and 22 (including 19 and 22) will conduct social media screening. show all steps for probabilities please. answer parts a-c.arrow_forward
- Question: we know that for rt. (x+ys s ا. 13. rs. and my so using this, show that it vye and EIXI, EIYO This : E (IX + Y) ≤2" (EIX (" + Ely!")arrow_forwardTheorem 2.4 (The Hölder inequality) Let p+q=1. If E|X|P < ∞ and E|Y| < ∞, then . |EXY ≤ E|XY|||X|| ||||qarrow_forwardTheorem 7.6 (Etemadi's inequality) Let X1, X2, X, be independent random variables. Then, for all x > 0, P(max |S|>3x) ≤3 max P(S| > x). Isk≤narrow_forward
- Theorem 7.2 Suppose that E X = 0 for all k, that Var X = 0} x) ≤ 2P(S>x 1≤k≤n S√2), -S√2). P(max Sk>x) ≤ 2P(|S|>x- 1arrow_forwardThree players (one divider and two choosers) are going to divide a cake fairly using the lone divider method. The divider cuts the cake into three slices (s1, s2, and s3).If the chooser's declarations are Chooser 1: {s3} and Chooser 2: {s3}, which of the following is a fair division of the cake?arrow_forwardTheorem 1.4 (Chebyshev's inequality) (i) Suppose that Var X x)≤- x > 0. 2 (ii) If X1, X2,..., X, are independent with mean 0 and finite variances, then Στη Var Xe P(|Sn| > x)≤ x > 0. (iii) If, in addition, X1, X2, Xn are identically distributed, then nVar Xi P(|Sn> x) ≤ x > 0. x²arrow_forward
- Theorem 2.5 (The Lyapounov inequality) For 0arrow_forwardTheorem 1.6 (The Kolmogorov inequality) Let X1, X2, Xn be independent random variables with mean 0 and suppose that Var Xk 0, P(max Sk>x) ≤ Isk≤n Σ-Var X In particular, if X1, X2,..., X, are identically distributed, then P(max Sx) ≤ Isk≤n nVar X₁ x2arrow_forwardTheorem 3.1 (The Cauchy-Schwarz inequality) Suppose that X and Y have finite variances. Then |EXYarrow_forward
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