机构地区: 苏州大学数学科学学院,江苏苏州215006
出 处: 《大学数学》 2017年第4期66-68,共3页
摘 要: 随机变量序列的依概率收敛必有依分布收敛,反之未必成立.若极限随机变量服从退化分布,则两种收敛等价.自然地,若这两种收敛等价,是否有极限随机变量服从退化分布?给予该问题肯定的回答. Convergence in probability implies convergence in distribution, but the converse is not all true. If the limit random variable obeys degenerate distribution, then the two types of convergence are equivalent. It is natural to ask, if the two types of convergence are equivalent, whether the limit random variable obeys degenerate distribution or not? In the paper, we will give a positive answer.