An Instructor Has Given a Short Test Consisting of Two

question 18

Essay

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?

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Definitions:

Set Point

A theory suggesting that the body regulates its weight and energy balance around a biologically predetermined point.

Weight Change

Refers to the fluctuation of a person's body weight over time, which can result from factors such as diet, exercise, and health conditions.

Set Point For Body Weight

A theory suggesting that the body regulates its weight and body fat level with internal controls, aiming to maintain a particular weight.

Natural Point Of Stability

An equilibrium state to which a system naturally tends to return after being disturbed.