Question

An engineer is studying early morning trafic patterns at a particular intersection. The observation period begins at 5:30 am. Let X denote the arrival time of the first vehicle from the north-south direction; let Y denote the first arrival 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 f(x, y) = {1/x for 0<y<x<1 and 0 otherwise. Find the correlation coefficient of X and Y and interpret its value within this context.

Answer 1

Hence, correlation coefficient is



So the arrival of vehicles from the two directions are positively related with each other. Which means if time of one side trafic increases there will be increase in time of arrival from other side