1. Covariance (10 points) Suppose we have two random variables and . X can take on six values (1, 2, 3, 4, 5, 6) and Y can take on seven values (1, 2, 3, 4, 5, 6, 7). Calculate the covariance of random variables and , using the joint probabilities below:

1 2 3 4 5 6 7 1 0.03398716 0.01497496 0.04907765 0.00633376 0.02769399 0.0501174 0.01797557 2 0.03224175 0.02936135 0.04240043 0.00553131 0.04217874 0.043882 0.01823161 3 0.01856414 0.00927504 0.03112706 0.02130091 0.00098823 0.02132745 0.00982302 4 0.00400758 0.01368541 0.02774395 0.01481103 0.01263629 0.04788958 0.02357557 5 0.01428959 1.4051E-05 0.00570304 0.00162988 0.04057227 0.04901208 0.04319039 6 0.04461732 0.00915015 0.01149506 0.04877478 0.04966309 0.00741254 0.00373281

1. Covariance (10 points) Suppose we have two random variables X and Y. X can take on six values (1,2,3,4,5,6) and Y can take on seven values (1,2,3,4,5,6, 7). Calculate the covariance of random variables X and Y, using the joint probabilities below: Y f(x,y) 1 2 3 1 2 3 4 5 6 7 0.03398716 0.01497496 0.04907765 0.00633376 0.02769399 0.0501174 0.01797557 0.03224175 0.02936135 0.04240043 0.00553131 0.04217874 0.043882 0.01823161 0.01856414 0.00927504 0.03112706 0.02130091 0.00098823 0.021327450.00982302 0.00400758 0.01368541 0.02774395 0.01481103 0.012636290.04788958 0.02357557 0.01428959 1.4051E-05 0.00570304 0.00162988 0.04057227 0.04901208 0.04319039 0.04461732 0.00915015 0.01149506 | 0.04877478 0.04966309 0.00741254 0.00373281 4 5 6