A stock solution of hydrochloric acid (HCl) 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...

Extracted text: A stock solution of hydrochloric acid (HCl) 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 a randomly selected bottle of solution. Assume that the joint probability density function of X and Y is given by { S c(x + y) 0 < x="">< 1="" and="" 0="">< y="">< 1="" f(x,y)="otherwise" find="" the="" value="" of="" the="" constant="" c="" so="" that="" f(x,y)="" is="" a="" joint="" density="" function.="" compute="" the="" marginal="" density="" function="" fx(x).="" a.="" b.="" compute="" the="" conditional="" density="" function="" fyx(y="" |="" x).="" c.="" d.="" compute="" the="" conditional="" expectation="" e(y="" |="" x="0.4)." are="" x="" and="" y="" independent?="" explain.="">