The probability distribution of a random variable X is given by
Then the variance of X is

Question

The probability distribution of a random variable X is given by Then the variance of X is

Aicharya · Accepted Answer

$\begin{aligned} \mathrm{E}(\mathrm{X})= & \sum x_{\mathrm{i}} \cdot \mathrm{P}\left(x_{\mathrm{i}}ight) \ = & 0(0.4)+1(0.3)+2(0.1)+3(0.1)+4(0.1) \ = & 1.2 \ \operatorname{Var}(\mathrm{X}) & =\mathrm{E}\left(\mathrm{X}^2ight)-[\mathrm{E}(\mathrm{X})]^2 \ & =0^2(0.4)+1^2(0.3)+2^2(0.1)+3^2(0.1) \ & +4^2(0.1)-(1.2)^2 \ & =0.3+0.4+0.9+1.6-1.44 \ & =1.76\end{aligned}$

The probability distribution of a random variable X is given by Then the variance of X is

Solution