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What is the mutual information I x Y of two random variables X and Y?
Proof that the mutual information I(X;Y) between two random variables X and Y is 0 if and only if X and Y are independent. On the Wikipedia of mutual information it says that I(X;Y)=0 if and only if X and Y are independent. I can proof that if X and Y are independent, then I(X;Y)=0, because p(x,y)=p(x)p(y).
When X and Y are statistically independent then mutual information I X Y is?
An important theorem from information theory says that the mutual informa- tion between two variables is 0 if and only if the two variables are statistically independent. The formal definition of the mutual information of two random variables X. and Y , whose joint distribution is defined by P(X, Y ) is given by.
How to calculate mutual information between two variables?
Definition The mutual information between two discreet random variables X,Y jointly distributed according to p(x,y) is given by I(X;Y) = X x,y p(x,y)log p(x,y) p(x)p(y) (24) = H(X)−H(X|Y) = H(Y)−H(Y|X) = H(X)+H(Y)−H(X,Y). (25) 4
How is mutual information measured in probability theory?
In probability theoryand information theory, the mutual information(MI) of two random variablesis a measure of the mutual dependencebetween the two variables. More specifically, it quantifies the “amount of information” (in unitssuch as shannons, commonly called bits) obtained about one random variable through observing the other random variable.
What is mutual information in discrete random variables?
Let’s now discuss another similar technique in the case of discrete random variables, the Conditional Mutual Information. Mutual Information (MI) in information theory describes the mutual dependency between two random variables.
The concept of mutual information is intimately linked to that of entropy of a random variable, a fundamental notion in information theory that quantifies the expected “amount of information” held in a random variable.