Patients are given a drug treatment and then evaluated. Symptoms either improve, degrade,
or remain the same with probabilities 0.4, 0.1, 0.5, respectively. Assume that four independent patients are treated and let X and Y denote the number of patients who improve or
degrade. Are X and Y independent? Calculate the covariance and correlation between X
and Y . [Ans: -0.16, -0.272]