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Chapter 8: Discrete Probability Distributions
313
Section Review
Next we will study the concept of expected values or the long term average
for a discrete random variable.
8-4 Expected Value for a Discrete Random Variable
A very important concept in probability is the idea of
expected values
. The
expected value for a random variable is the long-term mean or average value
of the random variable. If the random variable is observed over a long
period of time, the expected value should be close to the average value of the
observations generated by the random process. The larger the number of
observations, the closer the expected value will be to the average value of
the observations.
Expected Value
The definition of the expected value for a discrete random variable is given
next.
Definition: Expected Value for a Discrete Random Variable
The expected value for a discrete random variable
X
is the long term mean
value of the weighted average value of the random variable.
The expected value is usually denoted by
E
(
X
) and is obtained by computing
the following formula. The weights here will be the values of the
probabilities associated with the values of the random variable.
Theoretically, the expected value is equivalent to the mean,
of the
population for which the distribution represents.
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