21. In each case below, determine whether the random variable sequence f g Yn converges in probability and/or in mean square, and if so, define what is being converged to.

(a) Yj ¼ ð Þ j þ 5 1 Pj i¼1 Xi for j ¼ 1; 2; 3; ... ;

Xi 0

s iid BernoulliðpÞ

(b) Yj ¼ j

1 P j

i¼1

ð Þ Xi  l 2 for j ¼ 1; 2; 3; ... ;

Xi 0

s iid PoissonðlÞ