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Digital Picture Processing, 2nd Edition
book

Digital Picture Processing, 2nd Edition

by Azriel Rosenfeld, Avinash C. Kak
January 2014
Intermediate to advanced content levelIntermediate to advanced
435 pages
18h 42m
English
Morgan Kaufmann
Content preview from Digital Picture Processing, 2nd Edition
34
2
Mathematical Preliminaries
2.3.3 Conditional Densities
Consider two events A and B. As stated earlier, their intersection Α η Β is
also an event. The conditional probability of A, given that Β has occurred,
is defined by
»{A
I
Β) = &{A η B)I^(B) (71)
The conditional distribution P
f
{z\B) of a random variable f, assuming Β has
occurred, is defined as the conditional probability of the event {f ^ z};
that is,
P
f
{z\B)
= 0>{f^z\B} = 9{{t ^ ζ) η B)\9(B) (72)
where the numerator is the event consisting of all outcomes ω, such that
f (ω,) ^ ζ and ω
ί
e Β (73)
At the points of continuity of P
f
(z
\
B), the conditional density is defined as
p
f
(z\B) ...
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Publisher Resources

ISBN: 9780323139915