An instructor has given a short test consisting of two parts

An instructor has given a short test consisting of two parts. For a randomly selected student, let X = the number of points earned on the first part and Y = the number of points earned on the second part. Suppose that the joint pmf of X and Y is given in the accompanying t

p(x,y)

0

5

10

15

0

.02

.06

.02

.10

5

.04

.15

.20

.10

10

.01

.15

.14

.01

If the score recorded in the grade book is the total number of points earned on the two parts, what is the expected recorded score E(X + Y)?

      [ Choose ]            14.1            2            0.013            0.3            2.3            9.6      

If the maximum of the two scores is recorded, what is the expected recorded score?

      [ Choose ]            14.1            2            0.013            0.3            2.3            9.6      

Solution

The Expected score E(X+Y)=0*0.02+5*0.06+10*0.02+15*0.10+5*0.04+10*0.15+15*0.20+20*0.10+10*0.01+15*0.15+20*0.14+25*0.01

=14.1

If the maximum of the two scores is recorded, then also the expected number of recorded score will be 14.1