Graphics Programs Reference
In-Depth Information
Probability Density
Function
Probability Density
Function
λ
=0.5
λ
=2
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
0
0123456
0123456
x
x
a
b
Fig. 3.6
Probability density function
f
(
x
) of a Poisson distribution with different values for
λ.
a
λ
=0.5 and
b
λ
=2.
Normal or Gaussian Distribution
When
p
=0.5 (symmetric, no skew) and
N
|
, the binomial distribution ap-
proaches the
normal
or
gaussian distribution
with the parameters mean
µ
and standard deviation
(Fig. 3.7). The probability density function of a
normal distribution in the continuous case is
σ
and the cumulative distribution function is
The normal distribution is used when the mean is the most frequent and most
likely value. The probability of deviations is equal towards both directions
and decrease with increasing distance from the mean. The
standard normal
distribution
is a special member of the normal family that has a mean of
zero
and a standard deviation of
one
.
We transform the equation of the normal distribution by substitute
z
=(
x
-
µ
)/
σ
.
