With groups of sizes … adding to …, the average size is…

38 With groups of sizes $x_1,\dots ,x_n$ adding to $G$, the average size is ______. The chance of an individual belonging to group 1 is ______. The expected size of his or her group is $E(x)=x_1(x_1/G)+\cdots +x_n(x_n/G)$. * Prove $\sum x_i^2/G⩾G/n$.

With groups of sizes $x_1,\dots ,x_n$ adding to $G$, the average size is ______. The chance of an individual belonging to group 1 is ______. The expected size of his or her group is $E(x)=x_1(x_1/G)+\cdots +x_n(x_n/G)$. * Prove ${\sum }_1^n{x}_i^2/G\ge G/n$.

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §5.6 Properties of the Integral and Average Value, #38