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.
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:
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