Page 30 - Computational Statistics Handbook with MATLAB

16 Computational Statistics Handbook with MATLAB

It is obvious that the cumulative distribution function takes on values
between 0 and 1, so 0 ≤ Fx() ≤ 1 . A probability density function, along with
its associated cumulative distribution function are illustrated in Figure 2.2.

PDF CDF
0.4 1

0.8
0.3
0.6
f(x) 0.2 F(x)
0.4
0.1
0.2
0 0
−4 −2 0 2 4 −4 −2 0 2 4
X X

FI F U URE G 2. RE 2. 2 2
IG
F F II GU RE RE 2. 2. 2
2
GU
This shows the probability density function on the left with the associated cumulative
distribution function on the right. Notice that the cumulative distribution function takes on
values between 0 and 1.
For a discrete random variable X, that can take on values x 1 x 2 …, , , the
probability mass function is given by

()
,,
f x i = PX =( x i ); i = 12 … , (2.3)
and the cumulative distribution function is

,,
Fa() = ∑ fx i i = 12 … . (2.4)
();
x ≤ a
i

© 2002 by Chapman & Hall/CRC