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 ran- dom. Because the three weights sum to 1, a joint probability model for any two gives all the necessary information about the weight of the third type. Let Y1 denote the weight of the almonds in a selected car and Y2 denote the weight of cashews. Then the joint probability density function is (24yıy2, 0< yı< 1, 0< y2 < 1, yı + y2 < 1 0, fV1, y2) = elsewhere ) Find the Cov(Y1, Y2) then interpret your answer. Jo it norsible for Yi and Y2 to be independent? Of course explain your answer..
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 ran- dom. Because the three weights sum to 1, a joint probability model for any two gives all the necessary information about the weight of the third type. Let Y1 denote the weight of the almonds in a selected car and Y2 denote the weight of cashews. Then the joint probability density function is (24yıy2, 0< yı< 1, 0< y2 < 1, yı + y2 < 1 0, fV1, y2) = elsewhere ) Find the Cov(Y1, Y2) then interpret your answer. Jo it norsible for Yi and Y2 to be independent? Of course explain your answer..
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question

Transcribed Image Text: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 ran-
dom. Because the three weights sum to 1, a joint probability model for any two gives all the necessary
information about the weight of the third type. Let Y1 denote the weight of the almonds in a selected can
and Y2 denote the weight of cashews. Then the joint probability density function is
24y1y2, 0<y1 < 1, 0 < y2 < 1, yi +y2 < 1
fV1,y2) =
0,
%3D
elsewhere
) Find the Cov(Y1, Y2) then interpret your answer.
Is it possible for Y1 and Y2 to be independent? Of course explain your answer..
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