Geoscience Reference
In-Depth Information
a
b
Fig. 3.4 a
Probability density function
f
(
x
), and
b
cumulative distribution function
F
(
x
),
of a uniform distribution with
N
=6. h e 6 discrete values of the variable
x
have the same
probability of 1/6.
i.e., the sum of all probabilities is one. h e maximum value of the cumulative
distribution function is therefore one.
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
. h e probability
for each face is 1/6. h e probability density function of this distribution is
h e 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 at er the Swiss scientist Jakob
Bernoulli (1654-1705), gives the discrete probability of
x
successes out of
N
trials, with a probability
p
of success in any given trial (Fig. 3.5). h e
probability density function of a binomial distribution is
