Let x1, ..., xn be i.i.d. with continuous distribution function F. Show that the distribution function of the order statistic x(m) is G(t) = ∑n k=m

(n k

)

F(t)

k

(1 − F(t))n−k

(Hint: for each t, the variable Nt = #{xi ≤ t} is binomial and verifies x(m) ≤

t ⇐⇒ Nt ≥ m).