Ans:
1)
P(y=0)=1-0.25-0.1-0.05
=1-0.4=0.6
2)
y | p(y) | cdf=P(Y<=y) |
0 | 0.6 | 0.6 |
1 | 0.25 | 0.85 |
2 | 0.1 | 0.95 |
3 | 0.05 | 1 |
Total | 1 |
3)
E(y)=0*0.6+1*0.25+2*0.1+3*0.05
=0+0.25+0.2+0.15=0.6
E(y^2)=0^2*0.6+1^2*0.25+2^2*0.1+3^2*0.05=1.1
Expected value of surcharge=E(Y+100Y^2)
=E(Y)+100*E(Y^2)
=0.6+100*1.1
=0.6+110=110.6
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