P BR BR PR EX( 1, 2, , ) ( )( )( 1 , )( 2 , )P PR P EX P BR PR EX P BR PR EX (10.3)
which may be performed in the following steps:
First the product P BR BR PR EX(1,2,)(1,)(2,P BR PR EX P BR PR EX) is considered and
the result is shown in Table 10.5.
PR G B
EX G B G B
BR1
G (1,0) (0.25,0.25) (0.25,0.25) (0,0)
B (0,0) (0.25,0.25) (0.25,0.25) (0,1)Table 10.5: Discrete conditional probability distribution for the condition of Bridge 1 and Bridge 2
conditional on production and execution quality ((x,y) are the probabilities corresponding
to the states G and B respectively for Bridge 2).
Thereafter the multiplication with is considered resulting in the joint probability
distribution given in
PPRPEX()(
)
)
PBR BR PREX(1, 2, , Table 10.6. Note that the probabilities given hereare no longer conditional.
PR G B
EX G B G B
BR1
G (0.81,0) (0.0225,0.0225) (0.0225,0.0225) (0,0)
B (0,0) (0.0225,0.0225) (0.0225,0.0225) (0,0.01)Table 10.6: Discrete joint probability distribution of the variables considered in the Bayesian Network
illustrated in Figure 1
From Table 10.6 various information can now be extracted by marginalization. It is e.g. seen
that PBR G PBR( 1 ) ( 2 G) 0.9 and that, not surprisingly PPRG PPRG()()0.9
as well. Also it is observed that based on Bayes’s rule it is possible to achieve the conditional
probability of the event >BRBBRB^21 ?, i.e.:
(2,1
(2 1 )
(1 )PBR BR B
PBR BR B
PBR B
)
(10.4)
In order to calculate this probability the joint probability distribution of the condition states of
the two bridges is first established as shown in Table 10.7.