For the following probability distribution :
| X | 1 | 2 | 3 | 4 |
| P(X) | $\frac{1}{10}$ | $\frac{1}{5}$ | $\frac{3}{10}$ | $\frac{2}{5}$ |
The value of $E(X^2)-[E(X)]^2$
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 1
$E(X)=EX_iP(X_i)$
$=\frac{1}{10}+\frac{2}{5}+\frac{9}{10}+\frac{8}{5}$
$=\frac{30}{10}=3$
$E(X^2)=EX_i^2P(X_i)$
$=\frac{1}{10}+\frac{4}{5}+\frac{27}{10}+\frac{32}{5}$
$=\frac{100}{10}=10$
$E(X^2)-(E(X))^2=10-3^2=1$