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Probability Distributions — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsProbability Distributions2 Marks
MCQ
A random variable X has the following probability distribution:
$\mathrm{X}=x_i$0135
P($\mathrm{X}=x$)0.20.50.20.1
Then, the variance of X is
  • A
    2.14
  • B
    2.54
  • C
    2.34
  • ✓
    2.24
✓

Answer

Correct option: D.
2.24
(D)
$\mathrm{E}(\mathrm{X})=\sum x_{\mathrm{i}} \cdot \mathrm{P}\left(x_{\mathrm{i}}\right)$
$\begin{aligned} & \quad=0(0.2)+1(0.5)+3(0.2)+5(0.1) -0+0.5+0.6+0.5 \\ & \quad=1.6 \\ & \begin{aligned} \text { Variance } & =\mathrm{E}\left(\mathrm{X}^2\right)-[\mathrm{E}(\mathrm{X})]^2 \\ & =(0)^2(0.2)+(1)^2(0.5)+(3)^2(0.2)+(5)^2(0.1)-(1.6)^2 \\ & =4.8-2.56=2.24\end{aligned}\end{aligned}$

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