A civil engineer is studying the live loads on a highway bridge. Let Y and Z denote the live load (in ten thousands of pounds) for traffic going east and west, respectively, at a randomly selected time of day.  Suppose these random variables have a joint distribution with density function f(y,z) = (1/400)yz2e–y/5–z/2, for y > 0, z > 0. If the loads are in opposite directions independent, what should the correlation coefficient and the regression curve of Y on Z be?

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