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

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