Two numbers are selected at random from the first six positive integers. If $X$ denotes the larger of two numbers, then $\operatorname{Var}(X)=$

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$\begin{array}{cccc}\mathbf{X}_{\mathbf{i}} & \mathbf{P}_{\mathbf{i}} & \mathbf{P}_{\mathbf{i}} \mathbf{X}_{\mathbf{i}} & \mathbf{P}_{\mathbf{i}} \mathbf{X}_{\mathbf{i}}{ }^2 \ \mathbf{1} & \frac{0}{15} & \mathbf{0} & \mathbf{0} \ \mathbf{2} & \frac{1}{15} & \frac{2}{15} & \frac{4}{15} \ \mathbf{4} & \frac{2}{15} & \frac{6}{15} & \frac{18}{15} \ 5 & \frac{3}{15} & \frac{12}{15} & \frac{48}{15} \ \mathbf{6} & \frac{4}{15} & \frac{20}{15} & \frac{100}{15} \ & \frac{5}{15} & \frac{30}{15} & \frac{180}{15}\end{array}$ $\overline{\sum p_i x_i=\frac{70}{15}} \quad \overline{\sum p_i x_i^2=\frac{350}{15}}$. $\begin{aligned} & \operatorname{Var}(x)=\sum p_i x_i{ }^2-\left(\sum p_i x_iight)^2 \ & =\frac{70}{3}-\frac{196}{9} \ & =\frac{210-196}{9}=\frac{14}{9}\end{aligned}$

Two numbers are selected at random from the first six positive integers. If $X$ denotes the larger of two…

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