【正确答案】由X的分布律可得
| P | 0.4 | 0.3 | 0.3 |
| X | -2 | 0 | 2 |
| 3X2+5 | 17 | 5 | 17 |
| -2X2-8 | -16 | -8 | -16 |
E(3X
2+5)=17×(0.4+0.3)+5×0.3=13.4,
E[(3X
2+5)
2]=17
2×(0.4+0.3)+5
2×0.3=209.8,
D(3X
2+5)=E[(3X
2+5)
2]-E
2(3X
2+5)=30.24,
E(-2X
2-8)=-16(0.4+0.3)-8×0.3=-13.6,
E[(-2X
2-8)
2]=(-16)
2×(0.4+0.3)+8
2×0.3=198.4,
D(-2X
2-8)=E(-2X
2-8)
2]-E
2(-2X
2-8)=13.44