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

Mean: $E(X)=3*{\frac 7 {30}}+5*{\frac 1 3}+7 * {\frac {13} {30}}={\frac {162} {30}}=5.4$

Variance: $V(X)=E(X^2)-E^2(X)=3^2*{\frac 7 {30}}+5^2*{\frac 1 3}+7^2*{\frac {13} {30}}-5.4^2={\frac {950} {30}}-{\frac {729} {25}}={\frac {1880} {750}}={\frac {940} {375}}\approx 2.51$

Standard deviation: ${\sigma}(X)=\sqrt{2.51} \approx1.58$