The consumption of two types of manufacturing goods (X and Y) follows a hypothetical joint probability density function as follows:

f x y c x y x y XY ( , ) = ( + ) < < < < 2 for 0 1 and 0 1 where x and y are normalized to the respective maximum value for all the houses. Determine the constant c such that fxy(x,y) is a legitimate joint density function. Evaluate the marginal density functions fX(x) and fY(y). Evaluate the probability that 0 < x < 0.5 and 0 < y < 0.25. Are the random variables statistically uncorrelated? Why?