Stated in terms of log probability, two events are independent if and only if the log probability of the joint event is the sum of the log probability of the individual events:
In information theory, negative log probability is interpreted as information content, and thus two events are independent if and only if the information content of the combined event equals the sum of information content of the individual events:
See Information content §Additivity of independent events for details. 1 and Eq. On the other hand, if the random variables are continuous and have a joint probability density function

f

X
Y
Z
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(
x
,
y
,
z
)

{\displaystyle f_{XYZ}(x,y,z)}

, then

X

{\displaystyle X}

and

Y
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{\displaystyle Y}

are conditionally independent given

Z

{\displaystyle internet
if
for all real numbers

x

{\displaystyle x}

,

y

{\displaystyle y}

and

z

{\displaystyle z}

such that

f

Z

(
z
)
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0

{\displaystyle f_{Z}(z)0}

. .

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