Casio ClassPad II Custom Commands

mu(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 mu function.

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

Example

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

\[f(v) = \left\{ \begin{array}{ll} \dfrac{1}{6 \pi} \sin \left( \sqrt{ \dfrac{v-30}{3} } \right) & 30 \leq v \leq 3 \pi^2 + 30 \\ \ 0 & \mathrm{elsewhere} \end{array} \right.\]

(2023 Methods Exam 2 Section B Question 4i)

Contributed by Nhan