设随机变量X的密度函数为f(x)=
【正确答案】正确答案：显然E(X)存在，且 E(x)=∫
-∞
+∞
xf(x)dx=∫
0
1
x
2
dx+∫
1
2
x(2一x)dx =
E(X
2
)=∫
-∞
+∞
x
2
f(x)dx=∫
0
1
x
3
dx+∫
1
2
x
2
(2一x)dx =
D(X)=E(X
2
)一[E(X)]
2
=
E(X
2
)=∫
-∞
+∞
x
2
f(x)dx=∫
0
1
x
3
dx+∫
1
2
x
2
(2一x)dx =
D(X)=E(X
2
)一[E(X)]
2
=
【答案解析】