INTRODUCTORY STATISTICS (LOOSELEAF)
3rd Edition
ISBN: 9780135163146
Author: Gould
Publisher: PEARSON
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Chapter 2, Problem 11SE
Arm spans (Example 3) According to the ancient Roman architect Vitruvius, a person’s arm span (the distance from fingertip to fingertip with the arms stretched wide) is approximately equal to his or her height. For example, people 5 feet tall tend to have an arm span of 5 feet. Explain, then, why the distribution of arm span for a class containing roughly equal numbers of men and women might be bimodal.
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6. Show that
1{AU B} = max{1{A}, I{B}} = I{A} + I{B} - I{A} I{B};
I{AB} = min{I{A}, I{B}} = I{A} I{B};
I{A A B} = I{A} + I{B}-21{A} I {B} = (I{A} - I{B})².
Theorem 3.5 Suppose that P and Q are probability measures defined on the same
probability space (2, F), and that F is generated by a л-system A. If P(A) = Q(A)
for all A = A, then P = Q, i.e., P(A) = Q(A) for all A = F.
6. Show that, for any random variable, X, and a > 0,
Lo P(x
-00
P(x < x
Chapter 2 Solutions
INTRODUCTORY STATISTICS (LOOSELEAF)
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