Is $P(A,B|X)=P(A|X)P(B|X)$ if $A$, $B$ are conditionally independent?
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Suppose I have two events $A$ and $B$ that are conditionally independent from each other. Is the following correct?$$P(A,B|X)=P(A|X)*P(B|X)$$
If so, what is this rule called?
probability probability-theory bayesian
asked Nov 19 at 22:46
pafnuti
212114
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up vote
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down vote
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Suppose I have two events $A$ and $B$ that are conditionally independent from each other. Is the following correct?$$P(A,B|X)=P(A|X)*P(B|X)$$
If so, what is this rule called?
probability probability-theory bayesian
asked Nov 19 at 22:46
pafnuti
212114
3
If you mean "conditionally independent given $X$", then yes: it's the definition. en.wikipedia.org/wiki/…
– Clement C.
Nov 19 at 22:57
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Suppose I have two events $A$ and $B$ that are conditionally independent from each other. Is the following correct?$$P(A,B|X)=P(A|X)*P(B|X)$$
If so, what is this rule called?
probability probability-theory bayesian
asked Nov 19 at 22:46
pafnuti
212114
Suppose I have two events $A$ and $B$ that are conditionally independent from each other. Is the following correct?$$P(A,B|X)=P(A|X)*P(B|X)$$
If so, what is this rule called?
probability probability-theory bayesian
probability probability-theory bayesian
asked Nov 19 at 22:46
pafnuti
212114
asked Nov 19 at 22:46
pafnuti
212114
asked Nov 19 at 22:46
pafnuti
212114
asked Nov 19 at 22:46
pafnuti
212114
asked Nov 19 at 22:46
pafnuti
212114
212114
3
If you mean "conditionally independent given $X$", then yes: it's the definition. en.wikipedia.org/wiki/…
– Clement C.
Nov 19 at 22:57
add a comment |
3
If you mean "conditionally independent given $X$", then yes: it's the definition. en.wikipedia.org/wiki/…
– Clement C.
Nov 19 at 22:57
3
3
If you mean "conditionally independent given $X$", then yes: it's the definition. en.wikipedia.org/wiki/…
– Clement C.
Nov 19 at 22:57
If you mean "conditionally independent given $X$", then yes: it's the definition. en.wikipedia.org/wiki/…
– Clement C.
Nov 19 at 22:57
add a comment |
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If you mean "conditionally independent given $X$", then yes: it's the definition. en.wikipedia.org/wiki/…
– Clement C.
Nov 19 at 22:57