The probability distribution of the discrete random variable X

The probability distribution of the discrete random variable X is shown in the table below. What is the expected value of X ?

1. 1/6
2. 1/3
3. 1
4. 2
5. 3 1/6

Answer

The correct answer is E.

The expected value of a random variable is its theoretical long-run average value.

E(X) = (1/6 x 0) + (1/12 x 1) + (1/4 x 2) + (1/12 x 3) + (1/12 x 4) + (0 x 5) + (1/3 x 6)

E(X) = 0 + 1/12 + 1/2 + 1/4 + 1/3 + 0 + 2

E(X) = (1 + 6 + 3 + 4 + 24)/12

E(X) = 38/12 = 19/6 = 3 1/6