Practicing Success
Let X be a random variable whose probability distribution is given by the table
Then variance of $x$ is |
$\sqrt{\frac{57}{3}}$ $\frac{19}{3}$ $4$ $\frac{67}{3}$ |
$\frac{19}{3}$ |
mean = $E(X) = ∑pixi = 1×\frac{1}{3}+3×\frac{1}{6}+5×\frac{1}{6}+7×\frac{1}{3}$ $E(X) =\frac{2+3+5+7}{6}=\frac{24}{6}=4=E(X)$ so $E(X^2) =∑pi{x_i}^2 =1×\frac{1}{3}+9×\frac{1}{6}+25×\frac{1}{6}+49×\frac{1}{3}$ $E(X^2) =\frac{2+9+25+98}{6}=\frac{134}{6}$ $σ^2$ (variance) = $E(X^2)-(E(X))^2$ $=\frac{134}{6}-4^2=\frac{67}{3}-16$ $=\frac{67-48}{3}=\frac{19}{3}$ |