
解:依题意,ξ的可能值为-6 000,3 000,12 000,5 000,14 000,16 000,
P(ξ=-6000)=0.052=0.0025,
P(ξ=3000)=2×0.2×0.05=0.02,
P(ξ=12000)=0.22=0.04,
P(ξ=5000)=2×0.75×0.05=0.075,
P(ξ=14000)=2×0.75×0.2=0.3,
P(ξ=16000)=0.752=0.5625.
ξ的分布列为
ξ | -6000 | 3000 | 12000 | 5000 | 14000 | 16000 |
P | 0.002 5 | 0.02 | 0.04 | 0.075 | 0.3 | 0.56 25 |
ξ的期望为
Eξ=-6000×0.02 5+3000×0.02+12000×0.04+5000×0.075+14 000×0.3+16 000×0.562 5
=14 100(元).