TABLE 1 Profits for Gotham City Covariance Type of Summer Hotel Profit Rainy Sunny -$1,000 $2,000 Umbrella Profit $4,500 -$500 EXAMPLE 9 Gotham City Summers Each summer in Gotham City is classified as being either a rainy summer or a sunny sum- mer. The profits earned by Gotham City's two leading industries (the Gotham City Hotel and the Gotham City Umbrella Store) depend on the summer's weather, as shown in Table 1. Of all summers, 20% are rainy, and 80% are sunny. Let H and U be the following ran- dom variables: H = profit earned by Gotham City Hotel during a summer U = profit earned by Gotham City Umbrella Store during a summer Find cov(HU). TABLE 1 Profits for Gotham City Covariance Type of Summer Hotel Profit Rainy Sunny -$1,000 $2,000 Umbrella Profit $4,500 -$500 EXAMPLE 9 Gotham City Summers Each summer in Gotham City is classified as being either a rainy summer or a sunny sum- mer. The profits earned by Gotham City's two leading industries (the Gotham City Hotel and the Gotham City Umbrella Store) depend on the summer's weather, as shown in Table 1. Of all summers, 20% are rainy, and 80% are sunny. Let H and U be the following ran- dom variables: H = profit earned by Gotham City Hotel during a summer U = profit earned by Gotham City Umbrella Store during a summer Find cov(HU)