A random variable X has the following probability distribution:
| X | −2 | −1 | 0 | 1 | 2 |
| P(X) | 0.2 | 0.1 | 0.3 | 0.2 | 0.2 |
The variance of X will be:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 1.89
The variance is found from \(\mathrm{Var}(X) = E(X^2) - [E(X)]^2\).
\(E(X) = (-2)(0.2) + (-1)(0.1) + 0(0.3) + 1(0.2) + 2(0.2)\)
\(= -0.4 - 0.1 + 0 + 0.2 + 0.4 = 0.1\)
\(E(X^2) = 4(0.2) + 1(0.1) + 0(0.3) + 1(0.2) + 4(0.2)\)
\(= 0.8 + 0.1 + 0 + 0.2 + 0.8 = 1.9\)
So
\(\mathrm{Var}(X) = 1.9 - (0.1)^2\)
\(= 1.9 - 0.01 = 1.89\)