Question

A random variable x is uniformly distributed over the interval (-4, 6). Find the standard deviation of x.

Answer 1

Answer:

The standard deviation is calculated to be 2.886 in the given interval

Explanation:

Uniform distribution in an interval [a,b] is defined by the function

$f(x)=\frac{1}{b-a}$

The variance of the distribution is given by

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

Hence the standard deviation is given by

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

Applying values we get

$\sigma =\frac{6-(-4)}{\sqrt{12}}\\\\\sigma = \frac{10}{\sqrt{12}}=2.886$