Answer to Question #168829 in Statistics and Probability for hah

Question

Find the variance and standard deviation of the probability distribution of the random variable X, which can take only the values 3,5, and 7, given that P (3) = (7)/(30),P(5) = (1)/(3),P(7) = (13)/(30)

Answer 1

In order to find the variance ( $\sigma^2$ ) of the given distribution, we will use the following formula:

$\sigma^2=\sum x^2\times p(x)-\mu^2$

In this example:

$\mu=\frac{27}{5}$

Now we will find the sum:

$\sum x^2\times p(x) = 3^2\times\frac{7}{30}+5^2\times\frac{1}{3}+7^2\times\frac{13}{30} = \frac{95}{3}$

Putting all together we have:

$\sigma^2=\sum x^2\times p(x)-\mu^2 = \frac{95}{3} - (\frac{27}{5})^2 = \frac{188}{75}$

Standard deviation: $\sigma = \sqrt{\sigma^2} = \sqrt{\frac{188}{75}} = 1.5832$