Beginning Statistics, 2nd Edition
2nd Edition
ISBN: 9781932628678
Author: Carolyn Warren; Kimberly Denley; Emily Atchley
Publisher: Hawkes Learning Systems
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Chapter 1.1, Problem 28E
To determine
To Explain:
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Students have asked these similar questions
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
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).
Theorem 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).
Chapter 1 Solutions
Beginning Statistics, 2nd Edition
Ch. 1.1 - Prob. 1ECh. 1.1 - Prob. 2ECh. 1.1 - Prob. 3ECh. 1.1 - Prob. 4ECh. 1.1 - Prob. 5ECh. 1.1 - Prob. 6ECh. 1.1 - Prob. 7ECh. 1.1 - Prob. 8ECh. 1.1 - Prob. 9ECh. 1.1 - Prob. 10E
Ch. 1.1 - Prob. 11ECh. 1.1 - Prob. 12ECh. 1.1 - Prob. 13ECh. 1.1 - Prob. 14ECh. 1.1 - Prob. 15ECh. 1.1 - Prob. 16ECh. 1.1 - Prob. 17ECh. 1.1 - Prob. 18ECh. 1.1 - Prob. 19ECh. 1.1 - Prob. 20ECh. 1.1 - Prob. 21ECh. 1.1 - Prob. 22ECh. 1.1 - Prob. 23ECh. 1.1 - Prob. 24ECh. 1.1 - Prob. 25ECh. 1.1 - Prob. 26ECh. 1.1 - Prob. 27ECh. 1.1 - Prob. 28ECh. 1.2 - Prob. 1ECh. 1.2 - Prob. 2ECh. 1.2 - Prob. 3ECh. 1.2 - Prob. 4ECh. 1.2 - Prob. 5ECh. 1.2 - Prob. 6ECh. 1.2 - Prob. 7ECh. 1.2 - Prob. 8ECh. 1.2 - Prob. 9ECh. 1.2 - Prob. 10ECh. 1.2 - Prob. 11ECh. 1.2 - Prob. 12ECh. 1.2 - Prob. 13ECh. 1.2 - Prob. 14ECh. 1.2 - Prob. 15ECh. 1.2 - Prob. 16ECh. 1.2 - Prob. 17ECh. 1.2 - Prob. 18ECh. 1.2 - Prob. 19ECh. 1.2 - Prob. 20ECh. 1.2 - Prob. 21ECh. 1.2 - Prob. 22ECh. 1.2 - Prob. 23ECh. 1.2 - Prob. 24ECh. 1.2 - Prob. 25ECh. 1.2 - Prob. 26ECh. 1.2 - Prob. 27ECh. 1.2 - Prob. 28ECh. 1.3 - Prob. 1ECh. 1.3 - Prob. 2ECh. 1.3 - Prob. 3ECh. 1.3 - Prob. 4ECh. 1.3 - Prob. 5ECh. 1.3 - Prob. 6ECh. 1.3 - Prob. 7ECh. 1.3 - Prob. 8ECh. 1.3 - Prob. 9ECh. 1.3 - Prob. 10ECh. 1.3 - Prob. 11ECh. 1.3 - Prob. 12ECh. 1.3 - Prob. 13ECh. 1.3 - Prob. 14ECh. 1.3 - Prob. 15ECh. 1.3 - Prob. 16ECh. 1.3 - Prob. 17ECh. 1.3 - Prob. 18ECh. 1.3 - Prob. 19ECh. 1.3 - Prob. 20ECh. 1.3 - Prob. 21ECh. 1.3 - Prob. 22ECh. 1.3 - Prob. 23ECh. 1.3 - Prob. 24ECh. 1.3 - Prob. 25ECh. 1.3 - Prob. 26ECh. 1.3 - Prob. 27ECh. 1.3 - Prob. 28ECh. 1.3 - Prob. 29ECh. 1.3 - Prob. 30ECh. 1.3 - Prob. 31ECh. 1.3 - Prob. 32ECh. 1.3 - Prob. 33ECh. 1.3 - Prob. 34ECh. 1.3 - Prob. 35ECh. 1.3 - Prob. 36ECh. 1.3 - Prob. 37ECh. 1.3 - Prob. 38ECh. 1.3 - Prob. 39ECh. 1.3 - Prob. 40ECh. 1.3 - Prob. 41ECh. 1.3 - Prob. 42ECh. 1.3 - Prob. 43ECh. 1.3 - Prob. 44ECh. 1.3 - Prob. 45ECh. 1.3 - Prob. 46ECh. 1.4 - Prob. 1ECh. 1.4 - Prob. 2ECh. 1.4 - Prob. 3ECh. 1.4 - Prob. 4ECh. 1.4 - Prob. 5ECh. 1.4 - Prob. 6ECh. 1.4 - Prob. 7ECh. 1.4 - Prob. 8ECh. 1.4 - Prob. 9ECh. 1.4 - Prob. 10ECh. 1.4 - Prob. 11ECh. 1.4 - Prob. 12ECh. 1.4 - Prob. 13ECh. 1.4 - Prob. 14ECh. 1.4 - Prob. 15ECh. 1.PA - Prob. 1PCh. 1.PA - Prob. 2PCh. 1.PA - Prob. 3PCh. 1.PA - Prob. 4PCh. 1.PA - Prob. 5PCh. 1.PA - Prob. 6PCh. 1.PB - Prob. 1PCh. 1.PB - Prob. 2PCh. 1.PB - Prob. 3PCh. 1.PB - Prob. 4PCh. 1.PB - Prob. 5PCh. 1.PB - Prob. 6PCh. 1.PB - Prob. 7PCh. 1.PB - Prob. 8PCh. 1.PB - Prob. 9PCh. 1.PB - Prob. 10PCh. 1.PB - Prob. 11PCh. 1.CR - Prob. 1CRCh. 1.CR - Prob. 2CRCh. 1.CR - Prob. 3CRCh. 1.CR - Prob. 4CRCh. 1.CR - Prob. 5CRCh. 1.CR - Prob. 6CRCh. 1.CR - Prob. 7CRCh. 1.CR - Prob. 8CRCh. 1.CR - Prob. 9CRCh. 1.CR - Prob. 10CRCh. 1.CR - Prob. 11CRCh. 1.CR - Prob. 12CRCh. 1.CR - Prob. 13CRCh. 1.CR - Prob. 14CRCh. 1.CR - Prob. 15CR
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