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An engineer is studying early morning traffic patters at a particular intersection. The observation period begins at 5:30 am. Let X denote the time of arrival of the first vehicle from the north-south direction; let Y denote the first arrival time from the east-west direction. Time is measured in fractions of an hour after 5:30 am. Assume that the density for (X, Y ) is given by
fXY (x,y)= 1/x 0
Required:
a. Find the curve of regression of X on Y. Is the regression linear?
b. Find the mean value of X when y = 0.5.
c. Find the curve of regression of Y on X. Is the regression linear?
d. Find the mean value of Y when x = 0.75.
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