
64 Data Analysis and Statistics for Geography, Environmental Science, and Engineering
When X is continuous
µ
X
EX xp xdx==
+∞
∫
[] () (3.11)
Note that the integration is over all values of X.
Example: Uniform in [0, 1]. In this case b = 1, a = 0. We know that p(x) = 1/(b − a) = 1.
µ
X
EX xdxx==
∫
[]
1
2
1
2
2
0
1
0
1
(3.12)
You need to recall integration from calculus.
The expected value or mean is a population concept. To calculate it we need its density or mass
function. The mean is not the same as the statistic known as the “sample mean” (Davis, 2002,
pp.28–29; p. 65; Carr, 1995). As explained in Chapter 1, the sample mean is the arithmetic average
of n