Pearson eText for An Introduction to Mathematical Statistics and Its Applications -- Instant Access (Pearson+)
6th Edition
ISBN: 9780137549375
Author: Richard Larsen, Morris Marx
Publisher: PEARSON+
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Chapter 9.4, Problem 6Q
Suppose
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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 9 Solutions
Pearson eText for An Introduction to Mathematical Statistics and Its Applications -- Instant Access (Pearson+)
Ch. 9.2 - Some states that operate a lottery believe that...Ch. 9.2 - As the United States has struggled with the...Ch. 9.2 - Amedical researcher believes that women typically...Ch. 9.2 - Among a number of beliefs concerning the so-called...Ch. 9.2 - The University of MissouriSt. Louis gave a...Ch. 9.2 - Prob. 6QCh. 9.2 - Poverty Point is the name given to a number of...Ch. 9.2 - A major source of mercury poisoning comes from the...Ch. 9.2 - Despite its complexity, the English language does...Ch. 9.2 - A company markets two br ands of latex...
Ch. 9.2 - Prob. 11QCh. 9.2 - Suppose that H0:X=Y is being tested against H1:XY,...Ch. 9.2 - An executive has two routes that she can take to...Ch. 9.2 - Prob. 14QCh. 9.2 - If X1,X2,...,Xn and Y1,Y2,...,Ym are independent...Ch. 9.2 - Let X1,X2,...,Xn and Y1,Y2,...,Ym be independent...Ch. 9.2 - A person exposed to an infectious agent, either by...Ch. 9.2 - For the approximate two-sample t test described in...Ch. 9.2 - Prob. 19QCh. 9.2 - Two popular forms of mortgage are the thirty-year...Ch. 9.3 - Case Study 9.2.3 was offered as an example of...Ch. 9.3 - Question 9.2.20 compared the rates of thirty-year...Ch. 9.3 - Among the standard personality inventories used by...Ch. 9.3 - In a study designed to investigate the effects of...Ch. 9.3 - Raynauds syndrome is characterized by the sudden...Ch. 9.3 - The bitter, eight-month baseball strike that ended...Ch. 9.3 - For the data in Question 9.2.8, the sample...Ch. 9.3 - Crosstown busing to compensate for de facto...Ch. 9.3 - Show that the generalized likelihood ratio for...Ch. 9.3 - Let X0,X2,...,Xn and Y1,Y2,...,Ym be independent...Ch. 9.4 - The phenomenon of handedness has been extensively...Ch. 9.4 - In a study designed to see whether a controlled...Ch. 9.4 - Water witching, the practice of using the...Ch. 9.4 - If flying saucers are a genuine phenomenon, it...Ch. 9.4 - In some criminal cases, the judge and the...Ch. 9.4 - Suppose H0:pX=pY is being tested against H1:pXpY...Ch. 9.4 - A total of 8605 students are enrolled full-time at...Ch. 9.4 - Prob. 8QCh. 9.4 - Prob. 9QCh. 9.4 - Compute 2ln(see Equation 9.4.1) for the nightmare...Ch. 9.5 - Historically, fluctuations in the amount of rare...Ch. 9.5 - Male fiddler crabs solicit attention from the...Ch. 9.5 - Construct two 99% confidence intervals for XY...Ch. 9.5 - Prob. 4QCh. 9.5 - Prob. 5QCh. 9.5 - Construct a 95% confidence interval for X2/Y2...Ch. 9.5 - One of the parameters used in evaluating...Ch. 9.5 - Prob. 8QCh. 9.5 - Flonase is a nasal spray for diminishing nasal...Ch. 9.5 - Construct an 80% confidence interval for the...Ch. 9.5 - Prob. 11QCh. 9.5 - For obese patients, there is an increased risk of...
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- 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_forwardTheorem 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_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_iosRecommended textbooks for you
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