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Binomial Distribution
In statistics the so-called binomial distribution describes the possible number of
times that a particular event will occur in a sequence of observations. The event
is coded binary, it may or may not occur. The binomial distribution is used when
a researcher is interested in the occurrence of an event, not in its magnitude. For instance,
in a clinical trial, a patient may survive or die. The researcher studies the number
of survivors, and not how long the patient survives after treatment. Another example is whether a person is ambitious or not. Here, the binomial distribution describes
the number of ambitious persons, and not how ambitious they are.
The binomial distribution is specified by the number of observations, n, and the probability
of occurence, which is denoted by p.
A classic example that is used often to illustrate concepts of probability theory,
is the tossing of a coin. If a coin is tossed 4 times, then we may obtain 0, 1, 2,
3, or 4 heads. We may also obtain 4, 3, 2, 1, or 0 tails, but these outcomes are
equivalent to 0, 1, 2, 3, or 4 heads. The likelihood of obtaining 0, 1, 2, 3, or 4 heads is,
respectively, 1/16, 4/16, 6/16, 4/16, and 1/16. In the figure on this page the distribution is shown with p = 1/2
Thus, in the example discussed here, one is likely to obtain 2 heads
in 4 tosses, since this outcome has the highest probability.
Other situations in which binomial distributions arise are quality control, public
opinion surveys, medical research, and insurance problems.
Poisson Limit
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