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 th…

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asked Jan 18, 2020 46.1k views

1 Answer

Dwwork · Answer 1 · 2020-01-23T05:23:01+0000

Answer:

The standard deviation of x is 2.8867

Explanation:

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

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

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

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

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

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

$s=\sqrt{(100)/(12) }$

s=√(8.3333)

s=2.8867