Probability distribution of random variable X is X -2 -1 0 1 2 P(X) 2…

The correct answer is Option (1) → 0

Given probability distribution:

$X$: -2, -1, 0, 1, 2

$P(X)$: $\frac{2}{11}, \frac{1}{11}, \frac{4}{11}, \frac{3}{11}, \frac{1}{11}$

Expected value $E(X) = \sum X \cdot P(X)$

$E(X) = (-2)\cdot \frac{2}{11} + (-1)\cdot \frac{1}{11} + 0 \cdot \frac{4}{11} + 1 \cdot \frac{3}{11} + 2 \cdot \frac{1}{11}$

$E(X) = \frac{-4 - 1 + 0 + 3 + 2}{11} = \frac{0}{11} = 0$