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Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.

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Distance between the product of marginal distributions and the joint distribution

Given a joint distribution $P(A,B,C)$, we can compute various marginal distributions. Now suppose: \begin{align} P1(A,B,C) &= P(A) P(B) P(C) \\ P2(A,B,C) &= P(A,B) P(C) \\ P3(A,B,C) &= P(A,B,C) \end …
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Distance between the product of marginal distributions and the joint distribution

I just find the following counter-example. Suppose $A,B,C$ are discrete variables. $A,B$ can each take two values while $C$ can take three values. The joint distribution $P(A,B,C)$ is: \begin{array} …
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