(1) An apartment manager decides to see if timely payment of rent is related to unpaid credit card balances. Using X as the number of unpaid credit card balances, and Y as the number of timely rent payments in the last four months, he examines his records and the credit reports of his renters and obtains the following results. X=0|X=1| X = 2 | X : = 3 Totals Y=0 0.01 0.01 0.06 0.03 0.11 Y = 1 0.02 0.04 0.07 0.04 0.17 Y = 2 0.03 0.08 0.09 0.04 0.24 Y = 3 0.05 0.11 0.08 0.02 0.26 Y = 4 0.13 0.05 0.03 0.01 0.22 Totals 0.24 0.29 0.33 0.14 1.00 (a) Find the probability of having renters with exactly 3 timely payments and 1 unpaid credit card balance. (b) Find the probability of having renters with less than 3 timely payments and 2 unpaid credit card balances. (c) Find the expected value (or mean) and variance of each random variable. (d) Are the events "unpaid credit card balance" and "timely rent payment" independent events? (e) Compute the covariance and correlation between two random variables.