Question

A random variable x is uniformly distributed over the interval (-4, 6). Find the standard deviation of x. (Note: Uniform distribution is a distribution where the PDF value is the same across all x values)

Answer 1

Answer:

The standard deviation of x is 2.8867

Step-by-step explanation:

The standard deviation of variable x that follows a uniform distribution is calculated as:

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

Where (a,b) is the interval where x is defined.

So, replacing a by -4 and b by 6, the standard deviation is:

$s = \sqrt{\frac{(6-(-4))^{2} }{12} }$

$s = \sqrt{\frac{(10)^{2} }{12} }$

$s=\sqrt{\frac{100}{12} }$

$s=\sqrt{8.3333}$

$s=2.8867$