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)

$\frac{1}{3} \sqrt{\frac{5}{2}}$

Answer 2

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, $\sigma = \sqrt{\frac{5}{18}} = \frac{1}{3} \sqrt{\frac{5}{2}}$