Casio ClassPad II Custom Commands

sd(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 sd function.

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

Example

Find the standard devation of \(x\) for the probability density function

\[\left\{ \begin{array}{ll} \dfrac{x}{500} & 0 \leq x < 20 \\ \dfrac{50-x}{750} & 20 \leq x \leq 50 \\ \ 0 & \text{elsewhere} \end{array} \right.\]

(2021 Methods Exam 2 Section B Question 4g)

Contributed by Nhan