Question

Find the variance and standard deviation of the probability distribution of a random variable x which can take only the values 1,2,3,4 and 5, given that P(1) = 3/10, P(2) = 1/10, P(3) = 2/10, P(4) = 3/10, P(5) = 1/10.

Answer 1

Mean: $\mu =\sum X\cdot P(X)=1\cdot 3/10+2\cdot 1/10+3\cdot 2/10+4\cdot 3/10+5\cdot 1/10=28/10=2.8$

Variance: $\sigma ^2=\frac{\sum(X-\mu)^2}{n}=\frac{1}{5}\big( (1-2.8)^2+(2-2.8)^2+(3-2.8)^2+(4-2.8)^2+(5-2.8)^2\big)=2.04$

Standard deviation: $\sigma =\sqrt{2.04}\approx 1.428$

Asnwer: variance is $2.04$ and standard deviation is $1.428$