CEM
834
STATISTICS
FALL
2005
II.
Probability Distribution Functions
In this section, we shall consider some important probability distribution functions.
These
functions represent a model for the experimental data or system of interest.
The model
may be good or bad, depending on the validity of the assumptions on which the model is
predicated.
Therefore, it is necessary to understand the assumptions in order to determine
under what conditions the model is an exact description of the experimental system and
under what conditions it is a reasonable approximation.
It is also of interest to determine
the properties of the various probability distribution functions and how calculations may
be performed with them.
A.
Binomial Distribution
Consider an experiment in which only two outcomes are possible, one that we shall
call a success and the other that we shall call a failure.
The probability for success in
an individual experiment or trial is p, and the probability for failure is
q
1
p
=

.
For
a series of n mutually independent trials, the overall probability of observing x
successes and
n
x

failures is
x
n
x
)
p
1
(
p
!
)
x
n
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 Fall '05
 MCGUFFIN
 Normal Distribution, Binomial distribution, Distribution function, µ, Lorentzian

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