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Statistics
Distribution
Binomial
Distribution
Chapter 4: Summary of Discrete Probability Distributions
Summary
Formulas
A binomial experiment satisfies the following conditions:
x=
1. The binomial experiment is repeated for a fixed number (n)
of independent trials.
2. There are only two possible outcomes—a success or a
failure.
3. The probability of a success remains constant for each trial.
4. The random variable x counts the number of successful
trails out of the n trials.
The parameters of a binomial distributions are
Geometric
Distribution
A geometric distribution is a discrete probability distribution of
a random variable x that satisfies the following conditions:
1. A trial is repeated until a success occurs.
2. The repeated trials are independent of each other.
3. The probability of success p is constant for each trial.
4. The random variable x represents the number of the trial in
which the first success occurs.
Calculator Steps
Use binompdf
p=
q=
Use binomcdf
q=
The probability of exactly x successes
in n trials is:
x=
Use 1-binomcdf
Use geometpdf
p=
q=
Use geometcdf
q=
The parameters of a geometric distribution are
Poisson
Distribution
The Poisson distribution is a discrete probability distribution of
a random variable x that satisfies the following conditions:
1. The experiment consists of counting the number of times an
event, x, occurs over a specified interval of time.
2. The probability of each event occurring is the same for each
interval.
3. The number of occurrences in one interval is independent of
occurrences in other intervals.
The parameters of a Poisson distribution are
4
The probability that the first success
occurs on trial number x is:
Use 1-geometcdf
x=
Use poissonpdf
=
Use poissoncdf
The probability of exactly x
occurrences in an interval is:
Use 1-poissoncdf