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The Joint entropy of two random variables is a direct extension of the definition of the entropy of a single random variable in this case the analytical expression for the entropy of two random variables X and Y is just the addition for all the elements uh in the alphabet of X and all the events in the alphabet of Y of the joint probability of this uh of these events times the logarith of the inverse of the joint probability with respect to the expression of the entropy of a single random variable We have replaced the entropy of X here and here and we have now a double addition because we are considering the alphabets of two random variables instead of the alphabet of a single single random variable but it is a direct extension of the concept of the entropy of a single random variable if we have h two independent random variables now the joint probability can be written as the product between the marginal probabilities of X and Y and if we replace this joint probabilities by th
