Uniform Probability Distribution The uniform distribution is a probability distribution in which the probability of a value occurring between two points, a and b, is the same as the probability between any other two points, c and d, given that the distribution between a and b is equal to the distance between c and d.

Uniform Probability Distribution CONTINUOUS UNIFORM DISTRIBUTION where: f(x) = Value of the density function at any x value a = Lower limit of the interval from a to b b = Upper limit of the interval from a to b

Uniform Probability Distributions (Figure 5-16) f(x) f(x) for 2  x  5 for 3  x  8 .50 .50 .25 .25 2 5 3 8 a b a b

Exponential Probability Distribution The exponential probability distribution is a continuous distribution that is used to measure the time that elapses between two occurrences of an event.

Exponential Probability Distribution EXPONENTIAL DISTRIBUTION A continuous random variable that is exponentially distributed has the probability density function given by: where: e = 2.71828. . . 1/ = The mean time between events ( >0)

Exponential Distributions (Figure 5-18) Lambda = 3.0 (Mean = 0.333) f(x) Lambda = 2.0 (Mean = 0.5) Lambda = 1.0 (Mean = 1.0) Lambda = 0.50 (Mean = 020) Values of x

Exponential Probability