An Introduction to Mathematical Statistics and Its Applications (6th Edition)

Published by Pearson
ISBN 10: 0-13411-421-3
ISBN 13: 978-0-13411-421-7

Chapter 3 Random Variables - 3.5 Expected Values - Questions - Page 153: 28

Answer

$\color{blue}{8}$

Work Step by Step

$\begin{align*} E(3X-4) &= 3E(X) - 4 & [\ \text{Corollary 3.5.1, p. 148}\ ] \\ &= 3\left(10\cdot \frac{2}{5}\right) - 4 & [\ \text{Theorem 3.5.1, p. 139,} \\ & & \; X\sim\text{Binomial}(n=10,p=2/5) \implies \\ && E(X) = np = (10)(2/5) \ ] \\ &= 12 -4 \\ \color{blue}{E(3X-4)}\ &\color{blue}{= 8} \end{align*}$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.