a) Let X= avg amount remains after eliminating one case
PX(x) =
1/5 X=(10+100+1000+10000)/4 *eliminating $1
1/5 X=(1+100+1000+10000)/4 *eliminating $10
1/5 X=(1+10+1000+10000)/4 *eliminating $100
1/5 X=(1+10+100+10000)/4 *eliminating $1000
1/5 X=(1+10+100+1000)/4 *eliminating $10000
E[X]=(1/5)*(10+100+1000+10000)/4 + (1/5)*(1+100+1000+10000)/4 +....=2222.2
b) Let X= amount he will take home after tax
PX(x)=
1/5 X=1*(1-30%) *the $1 dollar case will remain at last
1/5 X=10*(1-30%) *the $10 dollar case will remain at last
1/5 X=100*(1-30%) *the $100 dollar case will remain at last
1/5 X=1000*(1-30%) *the $1000 dollar case will remain at last
1/5 X=10000*(1-30%) *the $10000 dollar case will remain at last
E[X]=1555.54
