In Figure 4.2, the axes of the figures are labeled X and Y because the figures depict possible values of the random variables X and Y. However, the figure at the end of Example 4.1 depicts PX,Y (x, y) on axes labeled with lowercase x and y. Should those axes be labeled with the uppercase X and Y?
Figure 4.2
Example 4.1
Test two integrated circuits one after the other. On each test, the possible outcomes are a (accept) and r (reject). Assume that all circuits are acceptable with probability 0.9 and that the outcomes of successive tests are independent. Count the number of acceptable circuits X and count the number of successful tests Y before you observe the first reject. (If both tests are successful, let Y = 2.) Draw a tree diagram for the experiment and find the joint PMF of X and Y