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The mean of a probability distribution, also known as the expected value, represents the average outcome if an experiment is repeated many times. It's a measure of central tendency that weights each possible outcome by its probability of occurrence.
The calculator uses the expected value formula:
Where:
Explanation: The formula multiplies each possible outcome by its probability and sums all these products to find the weighted average.
Details: Calculating the mean of a probability distribution is fundamental in statistics, risk assessment, decision theory, and predictive modeling. It helps understand the central tendency of random phenomena and forms the basis for more complex statistical measures.
Tips: Enter values and their corresponding probabilities as comma-separated lists. Ensure probabilities are between 0 and 1 and sum to exactly 1. For example: Values: "1,2,3,4" and Probabilities: "0.1,0.2,0.3,0.4".
Q1: What's the difference between mean and expected value?
A: In probability theory, they're essentially the same concept. Expected value is the theoretical mean of a probability distribution.
Q2: Why must probabilities sum to 1?
A: This ensures all possible outcomes are accounted for, representing a complete probability distribution.
Q3: Can I use percentages instead of decimals?
A: No, probabilities must be entered as decimals between 0 and 1. For example, use 0.25 instead of 25%.
Q4: What if my probabilities don't sum to exactly 1?
A: The calculator will flag this as an error. All probabilities in a valid distribution must sum to 1.
Q5: How is this different from a simple average?
A: A simple average gives equal weight to all values, while the expected value weights each value by its probability.