A company sells boxes of savory items X and Y. The weight of each box is 1/2 kg, but the individual weights of the savory item X and savory item Y vary from box to box. For a randomly selected box, let X and Y have the joint density function f(x, y) ={ 24xy 0<=x<=1/2, 0<=y<=1/2, x+y<=1/2 { 0 elsewhere. (a) Find the marginal density for the weight of the Y savory item. (b) Find the probability that the weight of the Y savory item in a box is less than 1/8 of a 1/2kg if it is known that X savory item constitute 3/4 of the weight.

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