高等概率论的问题,Suppose we have in\x0cnitely many boxes numbered 1,

高等概率论的问题,
Suppose we have inx0cnitely many boxes numbered 1,2,3...We put balls in the
boxes one at a time.Each time,we independently put the ball in box k with probability pk,where pk x15>= 0 for all k and p1+p2+p3+.=1,Let Xn,k be the number of balls in box k after n balls have been placed in boxes.
(a) Prove that for each x0cfixed positive integer k,we have (Xn,k)/n -> pk a.s.
(b) Prove that as n->infinity,sup_{k}|(Xn,k)/n-pk|->0 a.s
第一题会做，感觉和函数列的一致收敛有关。