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Tagged with conditional-independence random-variable
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Undirected graphs and implications of independence (Wasserman chapter 18)
In Wasserman's All of Statistics chapter 18, he defines the following undirected graph:
Let $V$ be a set of random variables with distribution $\mathbb{P}$. Construct a graph with one vertex for each ...
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Conditional independence situation with three variables
Say we have three random variables, $X, Y$ and $Z$, where $X$ is independent of $Z$ (but not $Y$).
Does $E\bigg[ \dfrac{X}{f(Y,Z)} \bigg| Y \bigg] = E[X|Y] * E\bigg[ \dfrac{1}{f(Y,Z)} \bigg|Y \bigg]$?
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Does mutual independence of X, Y, Z implies conditional independence of X and Y, given Z
Given mutual independence of 3 r.v.s X, Y, Z, can we conclude that X and Y are independent, given Z?
Note that I am interested in case when all 3 r.v.s are mutually independent, not only pair X, Y.
In ...
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Given random variables $X,Y,Z$, under what conditions is $P(Y|X)=P(Y|X,Z)$?
From this link, where the statement is given for events and not random variables, I gather that for random variables $X,Y,Z$, $P(Y|X)=P(Y|X,Z)$ only if $P(Y,Z|X)=P(Y|X)P(Z|X)$? Does this imply that $Y$...
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