设F
1
(x)，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( )
【正确答案】
D
【答案解析】解析：因为f
1
(x)与f
2
(x)均为连续函数，故它们的分布函数F
1
(x)与F
2
(x)也连续．根据概率密度的性质，应有f(x)非负，且∫
-∞
+∞
f(x)dx=1．在四个选项中，只有D项满足． ∫
-∞
+∞
[f
1
(x)F
2
(x)+f
2
(x)F
1
(x)]dx =∫
-∞
+∞
[F
1
(x)F
2
(x)]’dx =F
1
(x)F
2
(x)|
-∞
+∞
=1—0=1， 故选项D正确．