Statistics
Expected value of discrete outcomes
Weight every outcome by its probability and add the products.
The Formula
E = p1 x x1 + p2 x2 + ... + pn x xn
Weight every outcome by its probability and add the products.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| E | Expected value | same as outcome | The probability weighted average of all outcomes. |
| xi | Outcome | same as outcome | The value of each possible result, profit or loss. |
| pi | Probability | decimal | The chance of that outcome as a decimal, so 25 percent is 0.25. |
What Each Symbol Means
Esame as outcome
Expected value
The probability weighted average of all outcomes.
xisame as outcome
Outcome
The value of each possible result, profit or loss.
pidecimal
Probability
The chance of that outcome as a decimal, so 25 percent is 0.25.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate expected value page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate Expected Value, filed under Math. Every number the guide produces comes from substituting into this one line.