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:
6 5.2 Find Cov(X,Y).
The correlation coefficient of X and Y, denoted by
Corr(X, Y), X,Y, or just , is defined by
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
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
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