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

Alumni Liaison

Basic linear algebra uncovers and clarifies very important geometry and algebra.

Dr. Paul Garrett