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 table. $$\begin{array} { c c c c c }
\hline p ( x , y ) & 0 & 5 & 10 & 15 \
\hline 0 & .02 & .06 & .02 & .10 \
\hline 5 & .04 & .15 & .20 & .10 \
\hline 10 & .01 & .15 & .14 & .01 \
\hline
\end{array}$$
a. 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)?
b. If the maximum of the two scores is recorded, what is the expected recorded score?

Question

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 table. $$\begin{array} { c c c c c } 
\hline p ( x , y ) & 0 & 5 & 10 & 15 \
\hline 0 & .02 & .06 & .02 & .10 \
\hline 5 & .04 & .15 & .20 & .10 \
\hline 10 & .01 & .15 & .14 & .01 \
\hline
\end{array}$$ 
a. 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)?
b. If the maximum of the two scores is recorded, what is the expected recorded score?

Quizplus · Accepted Answer

The Answer of 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 table. $$\begin{array} { c c c c c } 
\hline p ( x , y ) & 0 & 5 & 10 & 15 \
\hline 0 & .02 & .06 & .02 & .10 \
\hline 5 & .04 & .15 & .20 & .10 \
\hline 10 & .01 & .15 & .14 & .01 \
\hline
\end{array}$$ 
a. 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)?
b. If the maximum of the two scores is recorded, what is the expected recorded score?

An Instructor Has Given a Short Test Consisting of Two