Question

Use the following information to answer the next eight exercises. A distribution is given as $X~U(0,12)$.

What is the theoretical standard deviation?

Short answer

The theoretical standard deviation is$3.46$.

Step-by-step solution

Given information

A distribution is given as $X~U(0,12)$

Solution

For any random variable $X$which follows uniform distribution with parameter $(0,12)$, the theoretical standard deviation is shown below:

$\sigma =\sqrt{\frac{(b-a{)}^2}{12}}$

$=\sqrt{\frac{(12-0{)}^2}{12}}$

$=\sqrt{\frac{144}{12}}$

$=\sqrt{12}$

$=3.46$