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13. probability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths13. probability1 Mark
MCQ
If $m$ and $\sigma ^2$ are the mean and variance of random variable $x$, whose distribution is given by 

$\begin{array}{|l|l|l|l|l|l|} \hline X=x & 0  & 1  & 2 & 3  & 4 \\ \hline P(X=x) & \frac{1}{3} & \frac{1}{2} & 0 & \frac{1}{6} & 0 \\ \hline \end{array}$

, then

  • A
    $m = {\sigma ^2} = 2$
  • B
    $m = 1,{\sigma ^2} = 2$
  • ✓
    $m = {\sigma ^2} = 1$
  • D
    $m = 2,{\sigma ^2} = 1$
✓

Answer

Correct option: C.
$m = {\sigma ^2} = 1$
c
$\mathrm{m}=\sum \mathrm{P}_{\mathrm{i}} \mathrm{x}_{\mathrm{i}}=\frac{1}{2}+\frac{1}{2}=1$

$\sigma^{2}=\sum P_{i}\left(m-x_{i}\right)^{2}=\frac{1}{3}+\frac{4}{6}=1$

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