Let X be a discrete random variable and probability distribution X is
| X | −1 | 0 | 1 |
| P(X) | \(\displaystyle\frac{1}{2}\) | \(\displaystyle\frac{1}{5}\) | \(\displaystyle\frac{3}{10}\) |
Then E(X) is equal to:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(-\displaystyle\frac{1}{5}\)
The expected value is \(E(X) = \sum x\,P(X = x)\):
\( \displaystyle E(X) = (-1)\cdot\frac{1}{2} + 0\cdot\frac{1}{5} + 1\cdot\frac{3}{10} \)
\( \displaystyle = -\frac{5}{10} + \frac{3}{10} \)
\( \displaystyle = -\frac{2}{10} = -\frac{1}{5} \)