Solve the following questions (show your work): [Q1] 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.), (a) Draw a tree diagram for the experiment (3 pts) (b)Find the joint PMF Pxy(x, y) (5pts) (c) Find the marginal PMFS for the random variables X and Y (6 pts) (d) Are X and Y independent? Why? (5) (e) Find rxy and Cov(X, Y). (6)