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: 5


$\mu=3$ $\sigma=3$ $P(\mu \leq X \leq \mu + \sigma)\approx 0.2325$

Work Step by Step

We are given $f(x)=\frac{e^{-t/3}}{3}=\frac{1}{3}e^{-t/3}$ with $[0;\infty)$ The mean of the distribution: $\mu=\frac{1}{\frac{1}{3}}=3$ The standard deviation of X is $\sigma=\frac{1}{\frac{1}{3}}=3$ The probability that the random variable is between the mean and 1 standard deviation above the mean: $P(\mu \leq X \leq \mu + \sigma)=\int^{3}_{6}(\frac{e^{-t/3}}{3})dt=\frac{1}{3}.(-3)e^{-t/3}|^{6}_{3}\approx 0.2325$
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