Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 11 - Probability and Calculus - 11.1 Continuous Probability Models - 11.1 Exercises - Page 576: 29


a. $P(0\leq X \leq 2)\approx 0.423$ b. $P(1 \leq X \leq 3) \approx 0.207$ c. $P(X\geq 5)\approx .408$

Work Step by Step

We are given $f(x)=\frac{1}{2}(1+x)^{-3/2}; [0;\infty)$ a. $P(0\leq X \leq 2)$ $=\int^{2}_{0}\frac{1}{2}(1+x)^{-3/2}dx$ $=-(1+x)^{-1/2}|^{2}_{0}$ $\approx 0.423$ b. $P(1 \leq X \leq 3)$ $=\frac{1}{2}\int^{2}_{0}(1+x)^{-3/2}dx$ $=-(1+x)^{-1/2}|^{3}_{1}$ $\approx 0.207$ c. $P(X\geq 5)$ $=\frac{1}{2}\int^{\infty}_{5}(1+x)^{-3/2}dx$ $=-(1+x)^{-1/2}|^{\infty}_{5}$ $\approx .408$
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