6.19 Let the random variables Y1, Y2, . . . be independent and distributed as Bernoulli(i

−1), i ≥ 1. Show that



n i=1 Yi − log n √

log n

−→d N(0, 1).

(Hint: You may recall that



n i=1 i

−1 − log n converges to a limit known as Euler’s constant. The actual value of the constant does not matter.)