Calculus with Applications (10th Edition)

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

Chapter 11 - Probability and Calculus - 11.3 Special Probability Density Functions - 11.3 Exercises - Page 597: 6


$\mu=10$ $\sigma =10$ $P(\mu \leq X \leq \mu + \sigma)\approx 0.2325$

Work Step by Step

We are given $f(x)=0.1e^{-0.1x}$ with $[0;\infty)$ The mean of the distribution: $\mu=\frac{1}{0.1}=10$ The standard deviation of X is $\sigma=\frac{1}{0.1}=10$ The probability that the random variable is between the mean and 1 standard deviation above the mean. $P(\mu \leq X \leq \mu + \sigma)=\int^{20}_{10}(0.1e^{-0.1t})dt=-e^{-0.1t}|^{20}_{10}\approx 0.2325$
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