5. (8 marks) A local company sells propane gas and kerosene gas for home use (usually for BBQs). The gasses are stored separately in two large tanks. Let the amount of propane gas in a tank be denoted as X, and the amount of kerosene gas in a tank be denoted as Y as measured in hundreds of liters. Suppose that the tanks are not relled each day, and the amounts in each tank are random variables with joint pdf: f($) k($2+y) 053:5 10;0$y$ 100 _ 0 otherwise Tanks are considered to be \"in need of lling\" if they are below 50% maximum capacity (maximum capacity, in hundreds of litres, is 10 and 100 for the two tanks respectively). a. Find the value of k. I). Find the probability that the propane tank is in need of lling, but the kerosene tank is not. c. Find the marginal distribution of Y