Expected Value Calculator — 公式
## How to Calculate Expected Value
### Formula
**E(X) = Sum of (xi * pi)**
The expected value is the long-run average outcome of a random variable. Multiply each possible outcome by its probability and sum the products. It represents the "center of gravity" of the probability distribution. The variance is E(X^2) - [E(X)]^2.
### Formula
**E(X) = Sum of (xi * pi)**
The expected value is the long-run average outcome of a random variable. Multiply each possible outcome by its probability and sum the products. It represents the "center of gravity" of the probability distribution. The variance is E(X^2) - [E(X)]^2.
计算示例
A game pays $10 with probability 0.2, $20 with probability 0.5, and $50 with probability 0.3.
- E(X) = 10*0.2 + 20*0.5 + 50*0.3
- = 2 + 10 + 15 = 27
- E(X^2) = 100*0.2 + 400*0.5 + 2500*0.3 = 20 + 200 + 750 = 970
- Var(X) = 970 - 27^2 = 970 - 729 = 241
- SD = sqrt(241) ≈ 15.5242