## 3.2 Mean, Variance, Standard Deviation, Interquartile Range

#### Expected Value (Mean)

- The expected value for a continuous random variable X is given by

E(X)=\int_{-\infty}^{+\infty} x \cdot f(x) d x=\int_{c}^{d} x \cdot f(x) d x

where [c,\ d] is the range of x where, outside of this range, we have f(x)=0.

- As usual E(X) can also be denoted as the Greek letter \mu (mu).
- Expanding the formula, we have