For the following probability distribution :
| X | 1 | 2 | 3 | 4 |
| P(X) | $\frac{1}{10}$ | $\frac{1}{5}$ | $\frac{3}{10}$ | $\frac{2}{5}$ |
$E(X^2)$ is equal to :
Answer & explanation
Correct answer: option 4
The correct answer is option (4) → 10
$E(X^2)=∑X^2P(X)$
$=1^2×\frac{1}{10}+2^2×\frac{1}{5}+3^3×\frac{3}{10}+4^2×\frac{2}{5}$
$=\frac{1}{10}+\frac{8}{10}+\frac{27}{10}+\frac{64}{10}=\frac{100}{10}=10$