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let us consider a image pattern recognition problem where there are
two classes to be distinguished: a class of dark objects and a
class of light objects
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further, the class of dark objects is subdivided into two
shapes: round dark objects and square dark objects
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it is desired to find the probability of a dark objects
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let the random variable X1 represent the number of
dark round objects, X2 represent the number of dark
square objects, and X3 denote the number of light
objects and x1, x2, x3 be the
values of these random variables for some image
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given that the objects are trinomially distributed and the
probability distribution function by
P(X1 = x1, X2 =
x2, X3 = x3/p) =
= f(x1, x2, x3/p)
where p is the unknown parameter of the distribution and
n = x1 + x2 + x3
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also the pattern recognizer can distinguish between a dark and
light object and can give the numbers in each class but cannot
differentiate between two dark objects