Question

Find the mean,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 and P(7)= 13/30.

Answer 1

Mean: $\mu=\frac{3+5+7}{3}=5.$

Variance: $\sigma^2=\frac{(3-5)^2+(5-5)^2+(7-5)^2}{3}=\frac{8}{3}\approx2.6667.$

Standard deviation: $\sigma=\sqrt{\frac{8}{3}}\approx1.6330.$