Consider a bundle of n parallel filament whose individual strengths are denoted by X 1 ,...,X n (nonnegative random variables). Also, let  be the ordered values of X 1 ,...,X n . The bundle strength...

Consider a bundle of n parallel filament whose individual strengths are denoted by X₁,...,X_n
(nonnegative random variables). Also, let
 be the ordered values of X₁,...,X_n. The bundle strength is then define by Daniels (1945) as

Consider the empirical distribution function F_n
as in (2.4.18) and show that

Hence, or otherwise, use (5.2.31), to verify that {Zn} is a nonnegative reverse sub martingale. Hence, use Theorem 6.4.3 to show that as