1. A business produces two products. The bivariate probability distribution of the quantities sold of the two products, each month, is as follows: X = quantity of product #1 3 6 9 0.2 0.05 0 Y = quantity of product #2 2 0.1 0.3 0.1 3 0 0.05 0.2 a. The expected quantity of product #1 sold is and the variance of the quantity of product #1 sold is The expected quantity of product #2 sold is and the variance of the quantity of product #2 sold is ONE DECIMAL. b. The expected quantity of product #1 sold given that the quantity of product #2 sold is 3 is The variance of the quantity of product #1 sold given that the quantity of product #2 sold is 3 is TWO DECIMALS. c. The covariance between the quantity of product #1 sold and the quantity of product #2 sold is . TWO DECIMALS. d. Net revenue per unit of product #1 sold is 40. Net revenue per unit of product #2 sold is 70. Fixed costs of operating the business are 30. Profits as a function of quantity of product #1 sold and quantity of product #2 sold are W= . EQUATION, NO SPACES. e. Expected profits are The variance of profits is NO DECIMALS (INTEGERS). f. Now change the bivariate probability distribution given above. Assume the marginal probability distributions of X and Y are the same as for the original bivariate probability distribution. But now assume that X and Y are independent. P(X = 6, Y