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Post Undeleted by Antonio Valerio Miceli-Barone
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Antonio Valerio Miceli-Barone
Antonio Valerio Miceli-Barone
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No.

Consider fourthree boolean variables: A, B, X, Y, where X and YA are i.i.d. Bernoulli with probabilty 0.5, while A = X and B = X $\oplus$ YA (that is, B is equal to the xor of X and YA).

It's easy to show that A and B areis also Bernoulli distributed with probabilty 0.5, and theyA and B are mutually independent, though obviously they aren't conditionally independent given X and Y.

No.

Consider four boolean variables: A, B, X, Y, where X and Y are i.i.d. with probabilty 0.5, while A = X and B = X $\oplus$ Y (that is, B is equal to the xor of X and Y).

It's easy to show that A and B are also Bernoulli distributed with probabilty 0.5, and they are mutually independent, though obviously they aren't conditionally independent given X and Y.

No.

Consider three boolean variables: A, B, X where X and A are i.i.d. Bernoulli with probabilty 0.5, while B = X $\oplus$ A (that is, B is equal to the xor of X and A).

It's easy to show that B is also Bernoulli distributed with probabilty 0.5, and A and B are mutually independent, though obviously they aren't conditionally independent given X.

Post Deleted by Antonio Valerio Miceli-Barone
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Antonio Valerio Miceli-Barone
Antonio Valerio Miceli-Barone
  • 283
  • 2
  • 11

No.

Consider four boolean variables: A, B, X, Y, where X and Y are i.i.d. with probabilty 0.5, while A = X and B = X $\oplus$ Y (that is, B is equal to the xor of X and Y).

It's easy to show that A and B are also Bernoulli distributed with probabilty 0.5, and they are mutually independent, though obviously they aren't conditionally independent given X and Y.