a. For f(x1, x2, x3) as given in Example 5.10, compute the joint marginal density function of X, and X3 alone (by integrating over x).

b. What is the probability that rocks of types 1 and 3 together make up at most 50% of the sample? [Hint: Use the result of part (a).]

c. Compute the marginal pdf of X, alone. [Hint: Use the result of part (a).]