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: 3


$\mu=0.25$ $\sigma=0.25$ $P(\mu \leq t \leq \mu + \sigma) \approx 0.2325$

Work Step by Step

We are given $f(x)=4e^{-4t}; [0;\infty]$ The mean of the distribution: $\mu=\frac{1}{4}=0.25$ The standard deviation of X is $\sigma=\frac{1}{4}=0.25$ The probability of the random variable between 1 standard deviation above the mean: $P(\mu \leq t \leq \mu + \sigma) = P(0.25 \leq t \leq 0.5) =\int^{0.5}_{0.25}4e^{-4t} =-e^{-4t}|^{0.5}_{0.25} \approx 0.233 \approx 0.2325$
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