A random variable X has the following probability distribution : ( array |c|c|c|c|c| X =x & 1 & 2 & 3 & 4 P ( X =x) & 0 1 & 0 2 & 0 3 & 0 4 array ) The mean and standard deviation of X are respectively

Step-by-step solution

The mean E(X) and standard deviation are calculated from the given probability distribution using standard formulas. E(X) = x_i P(X=x_i) = (1)(0.1) + (2)(0.2) + (3)(0.3) + (4)(0.4) = 3.0 E(X^2) = x_i^2 P(X=x_i) = (1)(0.1) + (4)(0.2) + (9)(0.3) + (16)(0.4) = 10.0 The variance is Var (X) = E(X^2) - [E(X)]^2 = 10.0 - 9.0 = 1.0 , giving standard deviation = 1.0 = 1 . The values E(X)=3 and =1 correspond to option B. Final answer: B