The expectation and variance describe the average value and spread of a probability distribution.
The expected value \(E(X)\) is the long-run average value of the random variable.
To calculate:
The variance measures the spread of the probability distribution.
The standard deviation is:
\[ \sigma = \sqrt{\mathrm{Var}(X)} \]| \(x\) | 0 | 1 | 2 |
|---|---|---|---|
| \(P(X=x)\) | 0.2 | 0.5 | 0.3 |
Mean:
\[ E(X)=0(0.2)+1(0.5)+2(0.3)=1.1 \]Variance:
\[ \sum x^2p = 0 + 0.5 + 1.2 = 1.7 \] \[ \mathrm{Var}(X)=1.7-(1.1)^2 \]