Question

Given the variable (X = 2, 4, 6, 8) and its corresponding probabilities {P(X) = 1/5, 3/10, 3/10, 1/5}, what will be the computed STANDARD DEVIATION

Answer 1

$$E(X)=2(\dfrac{1}{5})+4(\dfrac{3}{10})+6(\dfrac{3}{10})+8(\dfrac{1}{5})=5$$

$$E(X^2)=2^2(\dfrac{1}{5})+4^2(\dfrac{3}{10})+6^2(\dfrac{3}{10})+8^2(\dfrac{1}{5})=29.2$$

$$Var(X)=\sigma^2=E(X^2)-(E(X))^2$$

$$=29.2-(5)^2=4.2$$

$$\sigma=\sqrt{\sigma^2}=\sqrt{4.2}\approx2.04939$$