Question: The random variables X and Y , representing the weights of creams and toffees, respectively, in 1- kilogram boxes of chocolates containing a mixture of

The random variables X and Y , representing the weights of creams and toffees, respectively, in 1-

kilogram boxes of chocolates containing a mixture of creams, toffees, and cordials, have the joint density function f(x, y) = 24xy, 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, x + y ≤ 1, 0, elsewhere.

(a) Find the probability density function of the random variable Z = X + Y .

(b) Using the density function of Z, find the probability that, in a given box, the sum of the weights of creams and toffees accounts for at least 1/2 but less than 3/4 of the total weight.

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