Understanding Expected Value

Expected value (or weighted average) is a fundamental concept in probability theory and statistics, representing the average outcome of a random variable over many trials. It's calculated by summing the products of each possible value and its corresponding probability.

Calculation Formula

E[X] = Σ (xᵢ × P(xᵢ))

Example Calculation

Consider a dice roll: Values 1-6 each with probability 1/6:
E[X] = (1×1/6) + (2×1/6) + (3×1/6) + (4×1/6) + (5×1/6) + (6×1/6) = 3.5

Reference Table

Application	Typical Use
Probability Distributions	Calculating mean of discrete distributions
Decision Making	Comparing expected outcomes of different choices
Insurance	Premium calculations based on expected claims

Frequently Asked Questions

What if probabilities don't sum to 1?

The calculator will normalize probabilities to sum to 1, but show a warning. For accurate results, ensure probabilities sum to 1.

Can I use percentages instead of decimals?

Yes, enter 15% as either 0.15 or 15. The calculator automatically handles both formats.

How many decimal places are used?

Results are shown with 4 decimal places by default. Intermediate calculations use JavaScript's full precision.

Expected Value Calculator

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Expected Value Calculator - Weighted Average Tool

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