Cryptography Reference
In-Depth Information
=
Figure 4.5
The joint probability distribution of
n
random variables
X
1
,...,X
n
.
4.2.3
Conditional Probability Distributions
Let (Ω
,
Pr) be a discrete probability space and
]
>
0.If
X
is a
random variable in that space, then the
conditional probability distribution
P
X|A
of
X
given that event
A
an event with Pr[
A
A
holds is defined as follows:
P
X|A
(
x
)=Pr[
X
=
x
|A
]
Note that
P
X|A
is a regular probability distribution and hence that the proba-
bilities
P
X|A
(
x
) sumuptoone:
P
X|A
(
x
)=1
x
∈X
If the conditioning event involves another random variable
Y
defined on the
same sample space Ω, then the
conditional probability distribution
of
X
given that
Y
takes on a value
y
is defined as
