Asked by digital communication
Let X,Y be discrete random variables related as Y=g(X), where g is a deterministic function. The ordering of their entropies satisfies
H(X)≤H(Y), equality holds if g is a one to one mapping
H(X)≥H(Y), equality holds if g is a one to one mapping
H(X)≤H(Y), equality holds when H(X|g(X))=0
H(X)≥H(Y), equality holds when H(X|g(X))=0
H(X)≤H(Y), equality holds if g is a one to one mapping
H(X)≥H(Y), equality holds if g is a one to one mapping
H(X)≤H(Y), equality holds when H(X|g(X))=0
H(X)≥H(Y), equality holds when H(X|g(X))=0
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