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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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 Summer '08
 OULDHAYE
 Statistics, Correlation, Covariance, Probability, Variance

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