On entropy for mixtures of discrete and continuous variables

@article{Nair2006OnEF,
  title={On entropy for mixtures of discrete and continuous variables},
  author={Chandra Nair and Balaji Prabhakar and Devavrat Shah},
  journal={CoRR},
  year={2006},
  volume={abs/cs/0607075}
}
Let X be a discrete random variable with support S and f : S → S be a bijection. Then it is wellknown that the entropy of X is the same as the entropy of f(X). This entropy preservation property has been well-utilized to establish non-trivial properties of discrete stochastic processes, e.g. queuing process [1]. Entropy as well as entropy preservation is well-defined only in the context of purely discrete or continuous random variables. However for a mixture of discrete and continuous random… CONTINUE READING

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