Suppose I have 3 random variables, $X1, X2,X3$. Define $Z$ as:
I want to force $Z$ to equal 1 for every "realization" of $X1,X2,X3$ ($X_i \sim Beta(a_i,b_i))$. As an example, let $X_i$ denote the percentage of votes a party will get. In a hypothetical country, there are only 3 parties. Therefore, $Z$ is the total percentage of votes, which equals to 100%. Statistically, how could someone force Z to equal 1, and by simulation or through an analytical expression derive the percentages of party A,B and C?