Question

give me the answer of variance and standard deviation of P(3)=7/30 P(5)=1/3 and P(7)=13/30 by following the steps

Answer 1

Mean: $\mu=3*\frac{7}{30}+5*\frac{1}{3}+7*\frac{13}{30}=\frac{162}{30}=\frac{27}{5}=5.4.$

Variance: $\sigma^2=3^2*\frac{7}{30}+5^2*\frac{1}{3}+7^2*\frac{13}{30}-(\frac{27}{5})^2=\frac{188}{75}\approx 2.5067.$

Standard deviation: $\sigma=\sqrt{\frac{188}{75}}\approx 1.5832.$