Entropy Calculator

About Entropy Calculator

Welcome to our Entropy Calculator, a user-friendly tool designed to calculate the Shannon entropy of a discrete probability distribution. Entropy measures the unpredictability or average information content within a set of outcomes.

Features of the Entropy Calculator

• Step-by-Step Solutions: View a breakdown of how entropy is calculated.
• Visual Explanation: Two charts help illustrate both the probability distribution and each term of the entropy sum.
• Educational Clarity: Understand the role each outcome plays in total entropy.
• Easy Input: Enter probabilities in a comma-separated list.
• Accurate Computation: Combines symbolic and numeric methods for reliable results.

Understanding Entropy

For a discrete random variable \( X \) with possible outcomes \( x_i \) and corresponding probabilities \( p_i \), the Shannon entropy is given by:

\[ H(X) = - \sum_{i} p_i \log\bigl(p_i\bigr) \]

This measures the average level of “surprise” or uncertainty in the distribution.

How to Use the Entropy Calculator

• Enter probabilities in a comma-separated list (e.g., 0.2, 0.3, 0.5).
• Confirm the probabilities sum to 1.
• Click on "Compute Entropy" for a step-by-step solution and charts.

Applications of the Entropy Calculator

• Information Theory: Understand core concepts of randomness and data encoding.
• Data Science & Statistics: Measure uncertainty or diversity in various data sets.
• Educational Use: Teach or learn the fundamentals of entropy calculation.

Why Use Our Entropy Calculator?

• Time-Saving: Rapidly compute entropy without manual summations.
• Intuitive: Clearly see how each probability contributes to the final entropy.
• Visual Learning: Two charts offer a direct sense of the distribution and its entropy terms.

Additional Resources

For deeper exploration, check out:

• Entropy (Information Theory) - Wikipedia
• Information Theory - Khan Academy

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