STAT 3201 Lecture 24: Stats 4.17.17
17 Apr 2017
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Intuitively, we think of the dependence of two random variables y1 and y2 as implying that one variable either increases or decreases as the other one changes. Suppose that we know e(y1)= 1 and e(y2)= 2. Now consider the deviations (y1- 1) and (y2- 2) for any point (y1,y2). They both have the same sign and thus their product is positive. Point to the right of 1 give produce pairs of positive deviations and points to the left produce pairs of negative deviations. Thus, the average of the product of the deviations is large and positive. What if the points are sloped downwards. The average value of (y1- 1)(y2- 2) provides a measure of the linear dependence between y1 and y2. Definition: if y1 and y2 are random variables with means 1 and 2, respectively, the covariance of y1 and y2.
