A random variable X has the following probability distribution:
| X | 0 | 1 | 2 | 3 |
| P(X) | 0.2 | 0.1 | 0.3 | 0.4 |
The variance of X will be
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 1.29
The variance is \(\mathrm{Var}(X) = E(X^2) - [E(X)]^2\).
\(E(X) = 0(0.2) + 1(0.1) + 2(0.3) + 3(0.4)\)
\(E(X) = 0 + 0.1 + 0.6 + 1.2 = 1.9\)
\(E(X^2) = 0(0.2) + 1(0.1) + 4(0.3) + 9(0.4)\)
\(E(X^2) = 0 + 0.1 + 1.2 + 3.6 = 4.9\)
\(\mathrm{Var}(X) = 4.9 - (1.9)^2\)
\(\mathrm{Var}(X) = 4.9 - 3.61 = 1.29\)
Tip: 4.9 (Option (4)) is only \(E(X^2)\). A common slip is to stop there and forget to subtract \([E(X)]^2\).