申論題

9. When a certain method is used to collect a fixed volume of rock samples in a region, there are four resulting rock types. Let X₁, X₂, and X₃ denote the proportion by volume of rock types 1, 2, and 3 in a randomly selected sample (the proportion of rock type 4 is 1-X₁-X₂-X₃, so a variable X₄ would
be redundant). If the joint probability density function (pdf) of X₁, X₂, X₃ is

(a) Find the value of k. (5%)