Question: A nut company markets cans of deluxe mixed nuts containing almonds, cashews, and peanuts. Suppose the net weight of each can is exactly one pound, but the weight contribution of each type of nut is random. Because the three weights sum to 1, a joint probability model for any two gives all necessary information about the weight of the third type. Let Y₁ = the weight of almonds in a selected can and Y₂ = the weight of cashews. Then the joint probability density function is:

F(y₁,Y₂)={24y₁y₂, 0 ≤ y₁ ≤ 1, 0 ≤ y₂ ≤ 1, y₁ + y₂ ≤ 1

Find the Cov(Y₁,Y₂), then interpret your answer. Is it possible for Y₁ and Y₂ to be independent? Of course, explain your answer.