Show transcribed image text Problem 4) A company distributes boxes of three products: Product 1, Product 2, and Product 3. Suppose that the weight of each box is 1 kilogram, but the individual weights ofproducts 1, 2 and 3 vary from box to box. For a randomly selected box, let X and Y represent the weights of Product 1 and Product 2, respectively. Suppose that the joint density function of X and Y is å·¦1x, y) _{24ry, Otherwise.OSYS!, x + y S 1. a) Find the probability that in a given box Product 3 accounts for more than 1/2 of the weight. Find the marginal density for the weight of Product l kilogram if it is known that Product 1 constitute 3/4 ofthe weight. 2 in these boxes. purchased a box of products. b) c) Find the probability that the weight of Product 2 in a box is less than 1/8 of a d) Find the covariance between the weight of Product 1 and the weight of Product e) Find the expected weight for the sum of Product 1 and Product 2 if one

Problem 4) A company distributes boxes of three products: Product 1, Product 2, and Product 3. Suppose that the weight of each box is 1 kilogram, but the individual weights ofproducts 1, 2 and 3 vary from box to box. For a randomly selected box, let X and Y represent the weights of Product 1 and Product 2, respectively. Suppose that the joint density function of X and Y is å·¦1x, y) _{24ry, Otherwise.OSYS!, x + y S 1. a) Find the probability that in a given box Product 3 accounts for more than 1/2 of the weight. Find the marginal density for the weight of Product l kilogram if it is known that Product 1 constitute 3/4 ofthe weight. 2 in these boxes. purchased a box of products. b) c) Find the probability that the weight of Product 2 in a box is less than 1/8 of a d) Find the covariance between the weight of Product 1 and the weight of Product e) Find the expected weight for the sum of Product 1 and Product 2 if one