The following is a joint probability density function for two continuous random variables, X and Y:

f x y cx y x y XY ( , ) = for 0 < < 1 and 0 < < 1 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?