The Definite Integral And Probability

The probability P that an event will occur can be measured by the corresponding area under i probability density function. A probability density or frequency function is a continuous function fix such that:

1. f(x) > 0. Probability cannot be negative.

2. /^oo/W dx = 1. The probability of the event occurring over the entire range of x is 1.

3. P(a <x<b) = S f(x) dx. The probability of the value of x falling within the interval [a. b] is the value of the definite integral from a to b.

See Example 8 and Problems 15.32 and 15.33.

EXAMPLE 8. The time in minutes between cars passing on a highway is given by the frequency function f(t) = 2e~2t for t > 0. The probability of a car passing in 0.25 minute is calculated as follows:

Solved Problems

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