1. 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.

2. 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

3. 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

4. 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.

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

6. 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

7. Exponential Probability