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Probability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsProbability1 Mark
MCQ
Choose the correct answer from the given four options.
$\text{X}$ $1$ $2$ $3$ $4$
$\text{P}(\text{X})$ $\frac{1}{10}$ $\frac{1}{5}$ $\frac{3}{10}$ $\frac{2}{5}$
For the following probability distribution $E(X^2)$ is equal to :
  • A
    $3.$
  • B
    $5.$
  • C
    $7.$
  • ✓
    $10.$
✓

Answer

Correct option: D.
$10.$
$\text{E}(\text{X}^2)=\sum\text{X}^2\text{P}(\text{X})$
$=1\cdot\frac{1}{10}+4\cdot\frac{1}{5}+9\cdot\frac{3}{10}+16\cdot\frac{2}{5}$
$=\frac{1}{10}+\frac{4}{5}+\frac{27}{10}+\frac{32}{5}$
$=\frac{1+8+27+64}{10}=10$

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