DES - Definition of 'Variance'

Variance:

Given a probability distribution, the variance is defined as:

$$Var(X)\triangleq E\left[X^2\right]-{\left(E\left[X\right]\right)}^2$$

• The definition of expected value can be found here.

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~Example: Variance of the Exponential Distribution:

Knowing that the expected value of the exponential distribution:

$$E(X)=\frac{1}{\lambda }$$

and,

Where $\beta$ was is our $\frac{1}{\lambda }$

then:

$$\begin{array}{rl}Var(X)=& E\left[X^2\right]-{\left(E\left[X\right]\right)}^2\\ =& \frac{2}{{\lambda }^2}-\frac{1}{{\lambda }^2}\\ =& \frac{1}{{\lambda }^2}\end{array}$$

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