An engineer is studying early morning traffic patterns at a particular intersection. The observation period begins at 5:30 a.m. 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 a.m. Assume that the density for (X, Y) is given by f(x, y) = 1/x  0 < y < x < 1 Verify that this is a joint density for a two-dimensional random variable. Find P(X < 0.5 and Y < 0.25). Find the marginal densities for X and Y. Find P(X < 0.5). Find P(Y < 0.25). Are X and Y independent? Explain. Find E(X), E(Y), E(XY) and Cov(X, Y).

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