Calculate the probability-weighted average of a discrete variable. The result panel keeps expected value and its numerical trail together.
Expected value ΣxP(x) balances every outcome by its probability and describes a long-run average over repeated identical experiments.
The roles assigned to possible values and corresponding probabilities explain the operation that produces expected value.
It evaluates games, insurance losses, project outcomes, demand, and discrete decisions.
Probability entries must align with values and sum to one. Expectation need not be an observable outcome and does not show variability.
Values −5,10,25 with probabilities .5,.3,.2 have expectation −2.5+3+5=5.5.
Before accepting Expected value, restore the Expected Value inputs Possible values and Corresponding probabilities. Estimate Expected value independently. Then vary Corresponding probabilities alone and observe the new Expected Value output. This isolates the changed part of Expected Value.
Moving probability toward larger values raises expectation when normalization is preserved. That behavior gives the expected value output a built-in reasonableness test.
Discrete variance uses the same distribution to measure spread around this center. Writing “Expected value” beside the output prevents that mix-up.
Multiply each value by its matching probability and add the signed contributions without early rounding. Expected Value also leads to spread around expectation.
The number from Expected Value is incomplete without its convention. Record the roles Possible values, Corresponding probabilities, together with whether positions are distinguishable, events may overlap, or trials are replaced. Those facts define the sample space and cannot be recovered reliably from a copied result alone.
For Expected Value, use a boundary case such as zero events, one object, certainty, or impossibility when it belongs to the model. A correct boundary result is a useful defense against an unnoticed indexing or probability-scale error.
Substitute the Expected Value solution into Possible values. This Expected Value check rejects false Expected Value branches and forbidden denominators.
Choose an easy Possible values value before running Expected Value. Predict Corresponding probabilities, then compare it with the Expected Value output.
No.
Yes.
They describe the full distribution.
No; it is a long-run average.