For the following probability distribution of a random variable X , the Expected value and Variance of X are respectively X = x 1 2 3 P(X = x) 1/5 2/5 2/5

Step-by-step solution

The expected value of X is given by E(X) = x_i P(x_i) E(X) = 1 1 5 + 2 2 5 + 3 2 5 = 1 5 + 4 5 + 6 5 = 11 5 The expected value of X^2 is given by E(X^2) = x_i^2 P(x_i) E(X^2) = 1^2 1 5 + 2^2 2 5 + 3^2 2 5 = 1 5 + 8 5 + 18 5 = 27 5 The variance of X is given by Var(X) = E(X^2) - (E(X))^2 Var(X) = 27 5 - ( 11 5 )^2 = 27 5 - 121 25 = 135 - 121 25 = 14 25 Answer: 11 5 , 14 25