November 2012
Intermediate to advanced
794 pages
22h 9m
English
book
Probability, Random Variables, and Random Processes: Theory and Signal Processing Applications
by John J. Shynk
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2.8 BASIC PROBABILITY RESULTS
The following propositions follow from the three axioms of probability. They also illustrate how to rearrange a problem statement in terms of disjoint sets for which one can use Axiom 3 to derive the result.
Proposition 2.2. 
.
Proof. Since 
and 
:
(2.45) 
which gives 
and 
.
Proposition 2.3. For event 
, P(Ec) = 1−P(E).
Proof. Since 
and 
:
(2.46) 
which can be rewritten as P(Ec) = 1−P(E).
Proposition 2.4. If , then .
Proof. Since F contains E, it can be partitioned in ...
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