# Binomial Distribution - HP F2226A - 48GII Graphic Calculator User Manual

Graphing calculator.

Discrete probability distributions
A random variable is said to be discrete when it can only take a finite number
of values. For example, the number of rainy days in a given location can be
considered a discrete random variable because we count them as integer
numbers only. Let X represent a discrete random variable, its probability mass
function (pmf) is represented by f(x) = P[X=x], i.e., the probability that the
random variable X takes the value x.
The mass distribution function must satisfy the conditions that
and
A cumulative distribution function (cdf) is defined as
Next, we will define a number of functions to calculate discrete probability
distributions.
We suggest that you create a sub-directory, say,
HOME\STATS\DFUN (Discrete FUNctions) where we will define the
probability mass function and cumulative distribution function for the binomial
and Poisson distributions.

## Binomial distribution

The probability mass function of the binomial distribution is given by
f
(
n
,
p
,
x
)
n
where (
) = C(n,x) is the combination of n elements taken x at a time. The
x
values n and p are the parameters of the distribution. The value n represents
the number of repetitions of an experiment or observation that can have one
of two outcomes, e.g., success and failure. If the random variable X
represents the number of successes in the n repetitions, then p represents the
f(x) >0, for all x,
f
(
x
)
=
1
0 .
all
x
F
(
x
)
P
[
X
x
]
k
≤x
n
x
n
x
p
1 (
p
)
,
x
f
(
k
)
x
0
1 ,
2 ,
,...,
n
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