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**preview**shows half of the first page. to view the full**1 pages of the document.**8.5 Challenging Integral Applications

Probability Applications: Overview

Random Variables

Continuous random variables: their values change over the interval

Any continuous random variable has its probability density function , so that the probability of

lying between a and b is given by:

Usually for all

Since probabilities are measured from to ,

Mean Value

Mean value of any probability density function:

Exponential Distribution

This typically represents wait time, so that:

Normal Distributions

The probability density function:

, whose mean value is and the standard

deviation is

For small , the values of are centered around the mean

For large , the values of are spread out from the mean

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