Math Solutions

[See Steps] A nut company markets cans of deluxe mixed nuts containing almonds, cashews, and peanuts. Suppose the net weight of each can is exactly one

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 Y 1 = the weight of almonds in a selected can and Y 2 = the weight of cashews. Then the joint probability density function is:

F(y 1 ,Y 2 )={24y 1 y 2 , 0 ≤ y 1 ≤ 1, 0 ≤ y 2 ≤ 1, y 1 + y 2 ≤ 1

0, elsewhere

Find the Cov(Y 1 ,Y 2 ), then interpret your answer. Is it possible for Y 1 and Y 2 to be independent? Of course, explain your answer.

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