Question

The standard deviation of a uniformly distributed random variable between 0 and 1 is

• A. $\frac{1}{\sqrt{12}}$
• B. $\frac{1}{\sqrt{3}}$
• C. $\frac{5}{\sqrt{12}}$
• D. $\frac{7}{\sqrt{12}}$

Answer 1

The correct option is A $\frac{1}{\sqrt{12}}$

For a uniformly distributed random variable between a and b.

$\text{variance}=\frac{1}{12}(b-a{)}^2$

$\Rightarrow \text{Standard deriation}=\sqrt{\text{variance}}$

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

$=\frac{1}{\sqrt{12}}(b-a)$

$=\frac{1-0}{\sqrt{12}}(\because$ a = 0 & b = 1)
$=\frac{1}{\sqrt{12}}$