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# Specific Conditional Entropy

This online calculator calculates entropy of Y random variable conditioned on specific value of X random variable and X random variable conditioned on specific value of Y random variable given a joint distribution table (X, Y) ~ p

As you can find out from Conditional entropy calculator, conditional entropy H(Y|X) can be seen as the result of averaging H(Y|X=v) over all possible values v that X may take. So, the calculator below computes all H(Y|X=v) and all H(X|Y=v) given a joint distribution table (X, Y) ~ p, and displays them in two tables. You can find the formula below the calculator.

In order to calculate the specific conditional entropies you should enter the joint distribution matrix where the cell value for any i row and j column represents the probability of the ${x_i, y_j}$ outcome, $p_{(x_i, y_j)}$.

#### Specific Conditional Entropy

Digits after the decimal point: 2
H(Y|X)

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H(X|Y)

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### Specific conditional entropy formula

Specific conditional entropy of Y for the X taking the value v is the entropy of Y among only those outcomes in which X has the value v. That is,

$\mathrm {H} (Y|X=v)=-\sum _{y\in {\mathcal {Y}}}{P(Y=y|X=v)\log _{2}{P(Y=y|X=v)}}$

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