An elderly patient is examined for heart and lung problems using scores X and Y, respec- tively. A score has a value of 0 if there is no impairment, 1 if there is mild impairment, and? if there is severe impairment. Suppose that the distributions of X and Y in the population are as follows: P(X = 0) = 0.6, P(X = 1) = 0.3, P(X = 2) = 0.1; P(Y = 0) = 0.5, P(Y = 1) = 0.3, P(Y = 2) = 0.2. Let T = X + Y be the total score for heart and lung impairment for a patient. (a) List each of the 9 possible heart and lung score combinations. For each outcome compute the value of the total impairment score T and the associated probability, assuming independence between X and Y. (b) Obtain the distribution of T. (c) Find E(T) and Var (T). (d) Suppose that the heart and lung problems are not independent but are positively correlated. Would it change E(T)? Would it change Var (7)? Explain. A husband and wife inver