An environmental engineer measures the amount (by weight) of particulate pollution in air samples of a certain volume collected over two smokestacks at a coal-operated power plant. One of the stacks is equipped with a cleaning device. Let Y1 denote the amount of pollutant per sample collected above the stack that has no cleaning device and let Y2 denote the amount of pollutant per sample collected above the stack that is equipped with the cleaning device. Suppose that the relative frequency behavior of X and Y can be modeled by: f(x, y)=1; 0 ≤ x ≤ 2, 0 ≤ y ≤ 1, 2y ≤x

0 elsewhere

a. Find the covariance between X and Y.
b. Find the correlation between X and Y.
c. Find the expected value and variance of X - Y, the amount of pollutant removed by the cleaner.