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Unformatted text preview: ere ”<<” means “much smaller than”). For example, if P (A) = P (B ) = 0.001 and A and B are
independent, then P (A ∪ B ) = 0.002 − 0.000001 which is very close to the union bound, 0.002.
The union bound can be extended from a bound on the union of two events to a bound on the
union of m events for any m ≥ 2. The union bound on the probability of the union of a set of m
events is
P (A1 ∪ A2 ∪ · · · ∪ Am ) ≤ P (A1 ) + P (A2 ) + · · · + P (Am ).
(2.15)
The union bound for m events follows from the union bound for two events and argument by
induction on m. The union bound is applied in the following sections. 2.12.2 Network outage probability The network outage problem addressed here is one of many diﬀerent ways to describe and analyze
system reliability involving serial and parallel subsystems. An s − t network consists of a source
node s, a terminal node t, possibly some additional nodes, and some links that connect pairs of
nodes. Figure 2.12 pictures ﬁve such networks, network A through network E. Netwo...
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This note was uploaded on 02/09/2014 for the course ISYE 2027 taught by Professor Zahrn during the Spring '08 term at Georgia Institute of Technology.
 Spring '08
 Zahrn
 The Land

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