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# ACMMM167

## 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
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