For j = 1,2       n, let Xj be independent r.v.s defined as follows:

Then show that the Lindeberg condition (condition (12.24)) does not hold.

Recall that

and show that, for every É› > 0 and large n:

in order to conclude that

+j? with probability 1/12 j? each X; = {+j with probability 1/12 each with probability 1 1/6 1/6j.