The cumulative distribution function of a discrete random variable X is given by
Then $\mathrm{E}\left(\mathrm{X}^2\right)=$

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The cumulative distribution function of a discrete random variable X is given by Then $\mathrm{E}\left(\mathrm{X}^2\right)=$

Aicharya · Accepted Answer

$\begin{aligned} & \mathrm{P}(\mathrm{X}=-1)=\mathrm{F}(-1)=0.3 \ & \mathrm{P}(\mathrm{X}=0)=\mathrm{F}(0)-\mathrm{F}(-1)=0.7-0.3=0.4 \ & \mathrm{P}(\mathrm{X}=1)=\mathrm{F}(1)-\mathrm{F}(0)=0.8-0.7=0.1 \ & \mathrm{P}(\mathrm{X}=2)=\mathrm{F}(2)-\mathrm{F}(1)=1-0.8=0.2 \ & \begin{aligned} \mathrm{E}\left(\mathrm{X}^2ight) & =\sum x_{\mathrm{i}}^2 \cdot \mathrm{P}\left(x_{\mathrm{i}}ight) \ & =(-1)^2(0.3)+0^2(0.4)+1^2(0.1)+2^2(0.2) \ & =0.3+0+0.1+0.8 \ & =1.2\end{aligned}\end{aligned}$

The cumulative distribution function of a discrete random variable X is given by Then…

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