The Analysis of Biological Data
2nd Edition
ISBN: 9781936221486
Author: Michael C. Whitlock, Dolph Schluter
Publisher: W. H. Freeman
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Chapter 6, Problem 4PP
a.
To determine
To explain whether the given statement is true or false.
b.
To determine
To explain whether the given statement is true or false.
c.
To determine
To explain whether the given statement is true or false.
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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
Theorem 2.5 (The Lyapounov inequality)
For 0
Theorem 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
x2
Chapter 6 Solutions
The Analysis of Biological Data
Ch. 6 - Prob. 1PPCh. 6 - Prob. 2PPCh. 6 - Prob. 3PPCh. 6 - Prob. 4PPCh. 6 - Prob. 5PPCh. 6 - Prob. 6PPCh. 6 - Prob. 7PPCh. 6 - Prob. 8PPCh. 6 - Prob. 9PPCh. 6 - Prob. 10PP
Ch. 6 - Prob. 11PPCh. 6 - Prob. 12PPCh. 6 - Prob. 13PPCh. 6 - Prob. 14PPCh. 6 - Prob. 15APCh. 6 - Prob. 16APCh. 6 - Prob. 17APCh. 6 - Prob. 18APCh. 6 - Prob. 19APCh. 6 - Prob. 20APCh. 6 - Prob. 21APCh. 6 - Prob. 22APCh. 6 - Prob. 23APCh. 6 - Prob. 24APCh. 6 - Prob. 25APCh. 6 - Prob. 26APCh. 6 - Prob. 27APCh. 6 - Prob. 28APCh. 6 - Prob. 29APCh. 6 - Prob. 30AP
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