Use the probability distribution given in Table 2.2 to compute

(a) \(E(Y)\) and \(E(X)\);

(b) \(\sigma_{X}^{2}\) and \(\sigma_{Y}^{2}\); 

(c) \(\sigma_{X Y}\) and \(\operatorname{corr}(X, Y)\).

Table 2.2

TABLE 2.2 Joint Distribution of Weather Conditions and Commuting Times Rain (X = 0) No Rain (X = 1) Total Long commute (Y= 0) 0.15 0.07 0.22 Short commute (Y = 1) 0.15 0.63 0.78 Total 0.30 0.70 1.00