A random variable X has the following probability distribution:
| X | 0 | 1 | 2 |
| P(X) | 1/4 | 1/2 | 1/4 |
then, which of the following is correct?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → mean = 2 variance
The mean is \(E(X) = \sum x\,P(X = x)\):
\( \displaystyle E(X) = 0 \times \frac{1}{4} + 1 \times \frac{1}{2} + 2 \times \frac{1}{4} = 1 \)
\( \displaystyle E(X^2) = 0 \times \frac{1}{4} + 1 \times \frac{1}{2} + 4 \times \frac{1}{4} = \frac{3}{2} \)
The variance is \(E(X^2) - [E(X)]^2\):
\( \displaystyle \mathrm{Var}(X) = \frac{3}{2} - 1 = \frac{1}{2} \)
So the mean, 1, is twice the variance, \(\frac{1}{2}\): mean = 2 variance.