Answer to Question #310825 in Statistics and Probability for Rhelyn

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