Suppose that the net weight of each can is exactly

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Unformatted text preview: eanuts. Suppose that the net weight of each can is exactly 1lb, but the weight contribution of each type of nut is random. Consider the weight of almonds and the weight of cashews in a selected can and denote them by X and Y, respectively. Let the joint pdf for (X, Y) be: f(x,y) = 6 5.2 Find Cov(X,Y). Correlation The correlation coefficient of X and Y, denoted by Corr(X, Y), X,Y, or just , is defined by ρX,Y = Exercise 3: Find the correlation coefficient of X and Y in Exercise 2. 7 5.2 Propositions: If a and c are either both positive or both negative, Corr(aX+b, cY+d) = Corr(X,Y) For any two rv's X and Y, ‒1≤Corr(X,Y)≤1. If X and Y are independent, then ρ = 0, but ρ = 0 does not imply independence. ρ = 1 or ‒1 iff Y = aX + b for some numbers a and b. 8...
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