Chapter 6 – Continuous Probability Distributions
pp. 224228
Uniform Probability Distribution

If the probability of an event in any one given interval is equal to the probability of the
event in any other equal interval in a given larger interval, the random variable x is said
to have a
uniform probability distribution

The
uniform probability density function
is then:
f(x) = {1/(ba)} for a ≤ x ≤ b
,
0 elsewhere
(Equation 6.1 pp.225)

ex: if in an interval from120 to 140 minutes, the probability of an event in any one
minute interval is equal to the even occurring in any other oneminute interval, then f(x)
= {1/20} for 120 ≤ x ≤ 140, and 0 for elsewhere.
Area as a Measure of Probability

The area under the graph of f(x) in a uniform probability distribution is equal to the
probability. Area is equal to the height f(x) (probability) times the width of the interval

The total area under the graph of f(x) in a uniform probability distribution is equal to 1
(this holds true for all continuous probability distributions and is the analog of the
condition that the sum of the probabilities must equal 1 for a discrete probability
function)

The expected value of a uniform continuous probability distribution is
E(x) = (a + b) / 2
,
and the variance is
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 Fall '07
 Thornton
 Normal Distribution, Probability distribution, Probability theory, normal probability distribution, uniform probability distribution

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