I have scoured my textbook for the concept alluded to in the title of this thread; however, my textbook has failed, in that it provides no such information.
Does anyone know of some resources for this concept?
For instance, let me post a problem I am working on:
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.
p(x,y) 0 | 5 | 10 | 15
0 | 0.02| 0.06| 0.02| 0.10
5 | 0.04| 0.15| 0.20| 0.10
10| 0.01| 0.15| 0.14| 0.01
a) If the score recorded in the grade book is the total number of points earned on two parts, what is the distribution of $X+Y$ and what is the expected recorded score $E(X+Y)$
b) If the maximum of the two scored is recorded, what is the distribution of the maximum score $Max(X,Y)$ ad the expected maximum score $E(Max(X,Y))$
Now that I re-look at this question, I doubt whether I can solve any of it. At any rate, how do I find the distribution of $X+Y$?