单选题
设F
1
(x)与F
2
(x)为两个分布函数，其相应的概率密度f
1
(x)与f
2
(x)是连续函数，则必为概率密度的是______
A.f
1
(x)f
2
(x)．
B.2f
2
(x)F
1
(x)．
C.f
1
(x)F
2
(x)．
D.f
1
(x)F
2
(x)+f
2
(x)F
1
(x)．
A
B
C
D
【正确答案】
D
【答案解析】
解 由题意知F[*]，且F
1
(x)F
2
(x)为分布函数，那么[F
1
(x)F
2
(x)]'=f
1
(x)F
2
(x)+F
1
(x)f
2
(x)为概率密度，故选D．
有人问：不选A，B，C显然不可选)，可有反例?当然有，例如f
1
(x)=f
2
(x)=[*]，-∞＜x＜+∞，那么[*]，可见f
1
(x)f
2
(x)并非概率密度(注意题目要求f
1
(x)，f
2
(x)为连续函数，而[*]=[*]的积分手法熟吗?
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