Casio ClassPad II Custom Commands

var(f, x, a, b)

• f is an expression in terms of x
• x is a variable name
• a is the x-value of the starting point
• b is the x-value of the ending point

For fastest calculation time, the domain [a, b] should be as small as possible.

If f is a piecewise function it should be entered raw not as a user-defined function.

The integral of f over the domain [a, b] must equal 1, as this is assumed by the var function.

Returns the variance of the continuous probability distribution defined by the probability density function f over the domain [a, b].

Example

Find the expected value of \(x\) for the probability density function

\[\left\{ \begin{array}{ll} 0.2e^{-0.2x} & x \geq 0 \\ \ 0 & x < 0 \end{array} \right.\]

(2021 NHT Methods Exam 2 Section A Question 14)

Contributed by Nhan