Mathematics · Advanced university
Entropy of a uniform discrete distribution · formula reference
State the logarithm base; base 2 gives bits. The probabilities sum to one.
Formula
State the logarithm base; base 2 gives bits. The probabilities sum to one.
H = −Σp log₂p = log₂m for m equiprobable outcomes
Worked example
A discrete variable is uniformly distributed over 37 outcomes. Find its Shannon entropy in bits. Round the final result to 4 decimal places if needed. Answer in bits.
Each probability is 1/37. Hence H = −37(1/37)log₂(1/37) = log₂(37).
5.2095 bits
Prerequisites and checking
Algebra; calculus or linear algebra as appropriate to the topic. Keep units and rounding consistent. State the model conditions before applying the formula.
Further reading and review references
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