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Intermediate Mathematics - Binomial probability function and distribution

Binomial probability function and distribution

A random variable (X = the number of successes in a fixed number of
Bernoulli trials) has a binomial distribution. [1]

The Binomial distribution is the most frequently used discrete
probability distribution.

Note the following important characteristics of a binomially distributed
random variable:

* the outcome of a single trial has only two possible outcomes: success
and failure,

* there is a fixed, non-random, number of trials, n,

* the outcome of any trial should be independent of the outcomes of all
previous trials, and

* the probability of success, p, should not change from trial to
trial.The number of trials, n, and the probability of success, p, are
called the parameters [2] of the distribution.

A fair coin is tossed 4 times.

X = the number of heads in the four tosses.

Explain why X has a binomial distribution.

* Each toss can only result in one of two options: a head (success) or a
tail (failure)

* _n _= 4 is a fixed, non-random number of trials.

* The outcome of each toss is not influenced by the outcome of any
previous toss. That is, the trials are independent.

* The probability of success is constant from trial to trial:_ p_ = Pr (a