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.
A rough estimate made before calculating gives the finished expected value a useful plausibility check.
Values −5,10,25 with probabilities .5,.3,.2 have expectation −2.5+3+5=5.5.
Multiply each value by its matching probability and add the signed contributions without early rounding. Expected Value also leads to spread around expectation.
Before entering possible values and corresponding probabilities, identify what each field represents. Its label determines how the expected value relationship interprets the entry. The browser cannot supply missing unit context, so preserve that context in your notes.
Moving probability toward larger values raises expectation when normalization is preserved. That behavior gives the expected value output a built-in reasonableness test.
A final answer should carry enough context to be reusable: name it expected value, attach any applicable unit, and record the rounding point. If another person must reproduce the result, the supplied inputs in the fields and the displayed formula are more informative than the decimal alone.
Discrete variance uses the same distribution to measure spread around this center. Writing “Expected value” beside the output prevents that mix-up.
A useful note for this result contains the supplied inputs (possible values and corresponding probabilities), the answer label, and the chosen precision. That record can be checked without recreating the entire page state.
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.
No.
Yes.
They describe the full distribution.
No; it is a long-run average.