Question

Find the variance and standard deviation of the probability distribution of a random variable x which can take only the values 1,5,3,7,9 and 2 given that P(1) = 1/14 , P(5) = 2/14, P(3) = 4/14, P(7) = 3/14, P(9) = 1/14, P(2) = 3/14.

Answer 1

Mean:$\mu =\sum X\cdot P(X)=1\cdot 1/14+5\cdot 2/14+3\cdot 4/14+7\cdot 3/14+9\cdot 1/14+2\cdot 3/14=59/14$

Variance: $\sigma ^2=\frac{\sum(X-\mu)^2}{n}=\frac{1}{6}\big( (1-59/14)^2+(5-59/14)^2+(3-59/14)^2+(7-59/14)^2+(9-59/14)^2+(2-59/14)^2\big)=7.99$

Standard deviation: $\sigma =\sqrt{7.99}\approx 2.83$

Asnwer: variance is $7.99$ and standard deviation is $2.83$