Let ^{^}F_n(x) denote the empirical cdf of the sample X₁,X₂, . . .,X_n. The distribution of ^{^}F_n(x) puts mass 1/n at each sample item X_i. Show that its mean is ‾X. If T (F) = F⁻¹(1/2) is the median, show that T (^{^}Fn) = Q₂, the sample median.