If $\mathrm{P}(\mathrm{X}=2)=0.3, \mathrm{P}(\mathrm{X}=3)=0.4, \mathrm{P}(\mathrm{X}=4)=0.3$, then the…

If $\mathrm{P}(\mathrm{X}=2)=0.3, \mathrm{P}(\mathrm{X}=3)=0.4, \mathrm{P}(\mathrm{X}=4)=0.3$, then the variance of random variable X is
  1. 1.6
  2. 6.6
  3. 3.6
  4. 0.6

Solution

Given probability distribution is
$\begin{aligned} & \mathrm{E}(\mathrm{X})=\sum x_{\mathrm{i}} \mathrm{P}\left(x_{\mathrm{i}}\right) \\ & \quad=2(0.3)+3(0.4)+4(0.3) \\ & \begin{aligned} \mathrm{E}(\mathrm{X}) & =3 \\ \text { Variance } & =\mathrm{E}\left(x^2\right)-[\mathrm{E}(x)]^2 \\ & =2^2(0.3)+3^2(0.4)+4^2(0.3)-(3)^2 \\ & =0.6\end{aligned}\end{aligned}$

Asked in: MHT CET 2024 (04 May Shift 2)

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