# Binomial Distribution - HP 50g User Manual

Graphing calculator.

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
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 probability of
getting a success in any given repetition. The cumulative distribution function
for the binomial distribution is given by
f(x) >0, for all x,
F
(
x
)
n
n
,
p
,
x
)
⎜ ⎜
⎟ ⎟
x
f
(
x
)
1
0 .
all
x
P
[
X
x
]
k
x
n
x
p
1 (
p
)
f
(
k
)
x
,
x
0
1 ,
2 ,
,...,
n
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