A stock solution of hydrochloric acid (HCI) supplied by a certain vendor contains small amounts of several impurities, including copper and nickel. Let X denote the amount of copper and let Y denote the amount of nickel, in parts per ten million, in randomly selected bottle of solution. Assume the joint probability density function of X and Y is given by:

f(x, y) = K(x+y)2 0< x <1and 0
= 0 Otherwise

Find the probability that P(X?0.5 and Y?0.3)
Find the correlation coefficient between X and Y.