John is creating drinks for his Halloween party using his favorite grape flavoring powder and a soda-maker that creates carbonation. He measures the amount of grape flavor in the resulting drink as X, which is a continuous uniform random variable on the interval [0,10]. Then conditional on the amount of grape flavor, he measures the amount of carbonation as a continuous random variable YY. The conditional distribution of carbonation Y given grape flavor X=x is fY|X=x(y)=xe^xyfY|X=x(y)=xe^xy for y>0y>0. Find the joint probability density function of X and Y.