Probability distributions plays a key role in statistical
analysis. This is because standard theoretical distributions are
indeed the statistical models for different kinds of situations.
For example, consider a random experiment, the outcome of which
can be classified one of two mutually exclusive and exhaustive
ways, say, success or failure. Then if the experiment is
repeated n times, the binomial distribution is the model in
determining the probability of number of successes. The Poisson
distribution may serve as an excellent mathematical model in a
number of situations. The number of road accidents in some unit
of time, the number of insurance claims in some unit of time,
the number of telephone calls at a swichtboard in some unit of
time etc.. are all governed by the Poisson model. An another
example, the gamma distribution is frequently used as the
probability model for waiting times; for instance, in testing
bulbs until they fail, then if the random variable is the time
needed to obtain exactly failure