Question

For the probability distribution given by

$X=x_{i}$	0	1	2
$p_{i}$	$\frac{25}{36}$	$\frac{5}{18}$	$\frac{1}{36}$

the standard deviation $(\sigma)$ is

• A. $\sqrt{\frac{1}{3}}$
• B. $\frac{1}{3} \sqrt{\frac{5}{2}}$
• C. $\sqrt{\frac{5}{36}}$
• D. None of the above

Answer 1

Answer: (B)

Variance $=\sum x_{i} ^{2}p_{i} -\left(\sum x_{i} p_{i}\right)^{2} $
$= \left[0+ \frac{5}{18} + \frac{1}{9}\right] - \left[0+ \frac{5}{18} + \frac{2}{36}\right]^{2} = \frac{14}{36}- \frac{1}{9} = \frac{10}{36} = \frac{5}{18} $
Standard deviation, $ \sigma = \sqrt{\frac{5}{18}} = \frac{1}{3} \sqrt{\frac{5}{2}} $