Let X, ., X, be independent and identically distributed continuous random variables having distribution F. Let X,,, denote the ith smallest of X, X, and let F., be its distribution function. Show that

(a) F(x) = F(x) F-1-1(x) + F(x) F-1(x) === n-i

(b) Fin-(x) = F(x) +- Fin(x) n n (Hints: For part

(a) condition on whether X,

(c) What is the probability that the (n + 1)st ball drawn is white?