The probability distribution of a random variable X is given by X =x_i 0 1 2 3 4 P ( X =x_i ) 0.4 0.3 0.1 0.1 0.1 Then the variance of X is

Step-by-step solution

The variance of a random variable is given by Var (X) = E(X^2) - [E(X)]^2 . The expected value E(X) is computed as: E(X) = (0)(0.4) + (1)(0.3) + (2)(0.1) + (3)(0.1) + (4)(0.1) = 1.2 Similarly, the expected value of X^2 is: E(X^2) = (0^2)(0.4) + (1^2)(0.3) + (2^2)(0.1) + (3^2)(0.1) + (4^2)(0.1) = 3.2 Therefore, the variance is: Var (X) = 3.2 - (1.2)^2 = 1.76 Final answer: A