Titel_SS06

Figure 2.11: Illustration of A) a cumulative distribution function and B) a probability density function
for a continuous random variable.

For continuous random variables the probability density function is given by:



()

X

Fx

fx

x







(2.21)

The probability of an outcome in the interval x;ddx (^)  where is small, is given
by
dx
P x
 x x dx;  fX
z dx.
Random variables with a finite or infinite countable sample space are called discrete random
variables. For discrete random variables the cumulative distribution function is given as:
() ( )
i
XX
xx
Px p x

 i (2.22)
where ( )pXix is the probability density function given as:
pXi() (xPXxi) (2.23)
A discrete cumulative distribution function and probability density function is illustrated in
Figure 2.12.
x
x
A)
B)
1
PX(x)
x 1 x 2 x 3 x 4
x 1 x 2 x 3 x 4
pX(x)
Figure 2.12: Illustration of A) a cumulative distribution function and B) a probability density function
for a discrete random variable.