1. A candy company distributes boxes of chocolates with a mixture of creams, toffees and cordials. Suppose that the weight of each box is 1 kilogram, but the individual weights of the creams, toffees and cordials vary from box to box. For a randomly selected box, let X = weight of creams and Y =weights of the toffees and the pdf is described as:
f(x,y)= 24xy-for(0< or =x< or =1), (0< or =y< or =1), (x+y < or =1)
a. Find the probability that in a given box, the cordials amount for more than half of the weight
b. Find the marginal density for the weight of the creams
c. Find the probability that the weight of the toffees in a box of less than 1/8 of a kilogram given that creams constitute ¾ of the weight
2. Suppose that four inspectors at a film factory are suppose to stamp the expiration date on each package of film at the end of the assembly line. John, who stamps 20% of the packages, fails to stamp the expiration date once in every 200 packages. Tom, who stamps 60% of the packages, fails to stamp the expiration date once in every 100 packages. Jeff, who stamps 15% of the packages, fails to stamp the expiration date once in every 90 packages. And, Pat, who stamps the remaining packages, fails to stamp the expiration date once in every 200 packages. If a customer complains that her package of film does not show the expiration date, what is the probability that it was inspected by John?