Elementary Statistics (12th Edition)

Published by Pearson
ISBN 10: 0321836960
ISBN 13: 978-0-32183-696-0

Chapter 6 - Normal Probability Distributions - 6-4 Sampling Distributions and Estimators - Beyond the Basics - Page 283: 19



Work Step by Step

Evaluating the expressions at x=0, 0.5, 1: $P(0)=\frac{1}{2(2-2\cdot0)!(2\cdot0)!}=\frac{1}{2\cdot2!\cdot0!}=\frac{1}{4}$ $P(0.5)=\frac{1}{2(2-2\cdot0.5)!(2\cdot0.5)!}=\frac{1}{2\cdot1!\cdot1!}=\frac{1}{2}=\frac{2}{4}$ $P(1)=\frac{1}{2(2-2\cdot1)!(2\cdot1)!}=\frac{1}{2\cdot0!\cdot2!}=\frac{1}{4}$ The probabilities are equal to the ones in exercise 15, therefore they describe the sampling distribution found there.
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