Thinking Mathematically (7th Edition)
7th Edition
ISBN: 9780134683713
Author: Robert F. Blitzer
Publisher: PEARSON
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Chapter 6.1, Problem 5CVC
To determine
To fill: The statement: “ In the algebraic expression
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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 chooser's declarations are Chooser 1: {s3} and Chooser 2: {s3}, which of the following is a fair division of the cake?
Lemma:-
Let x = AX, Y° = By where A =
B=
0
Bo then the linear system X = AX Y = BY
are Linearly equivalent iff B=α.
Theorem 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.
x²
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