8.27 Suppose that 1, 2, . . . are independent such that i Bernoulli(pi ), where...

8.27 Suppose that ξ1, ξ2, . . . are independent such that ξi ∼ Bernoulli(pi ), where pi ∈ (0, 1), i ≥ 1. Show that as n→∞, 1 n

n i=1

ξ1 · · · ξi−1(ξi − pi )

−a→.s. 0.