Graphics Programs Reference
In-Depth Information
An example is a rolling die with
N
=6 faces. A discrete variable such as the
faces of a die can only take a countable number of values
x
. The probability
of each face is 1/6. The probability density function of this distribution is
The corresponding cumulative distribution function is
where
x
takes only discrete values,
x
=1, 2, …, 6.
Binomial or Bernoulli Distribution
A
binomial
or
Bernoulli distribution
, named after the Swiss scientist James
Bernoulli (1654-1705), gives the discrete probability of
x
successes out of
N
trials, with probability
p
of success in any given trial (Fig. 3.5). The prob-
ability density function of a binomial distribution is
Probability Density
Function p=0.1
Probability Density
Function p=0.3
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
012345
6
012345
6
x
x
a
b
Fig. 3.5
Probability density function
f
(
x
) of a binomial distribution, which gives the
probability
p
of
x
successes out of
N
=6 trials, with probability
a
p
=0.1 and
b
p
=0.3 of
success in any given trial.
