For the following probability distribution, the standard deviation of the random variable X is X 2 3 4 P(X=x) 0.2 0.5 0.3

Step-by-step solution

To compute the standard deviation of X , start with the expected value E(X) = x P(X=x) : E(X) = 2 0.2 + 3 0.5 + 4 0.3 = 0.4 + 1.5 + 1.2 = 3.1 Then find E(X^2) = x^2 P(X=x) : E(X^2) = 4 0.2 + 9 0.5 + 16 0.3 = 0.8 + 4.5 + 4.8 = 10.1 The variance is Var (X) = E(X^2) - [E(X)]^2 : Var (X) = 10.1 - (3.1)^2 = 10.1 - 9.61 = 0.49 Standard deviation is its square root: 0.49 = 0.7 Among the choices, 1 7 0.1428 is numerically closest, though units are not cubic.