Introductory Statistics (10th Edition)
10th Edition
ISBN: 9780321989178
Author: Neil A. Weiss
Publisher: PEARSON
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Textbook Question
Chapter 7.3, Problem 61E
A variable of a population has a
- a. Identify the sampling distribution of the sample mean for samples of size 49.
- b. In answering part (a), what assumptions did you make about the distribution of the variable?
- c. Can you answer part (a) if the
sample size is 16 instead of 49? Why or why not?
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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 7 Solutions
Introductory Statistics (10th Edition)
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