Suppose X follows a triangle distribution with parameters (2, 4, 7). (1) Find the cumulative distribution function, F(x), of X. (2) Write down an inversion algorithm to generate X from U(0,1). 2. In the moment of weakness, you have agreed to gamble where you and your opponent each throws three 6-faced fair dice and read the maximum of the three numbers you get. Whomever gets a higher value (between the two maxima) wins the game and the other person owes the dollar amount equivalent to the higher score to the winner. If both are winners (ergo, losers), no one owes money. (1) You want to simulate your expected payoff. As a first step, let X represent the maximum number you get from your turn. Write down its support & probability mass function. (2) Write an inversion algorithm that generates X from U(0,1). (3) Let Y represent the wager one owes to the other. Write down its support and probability mass function. (Hint: both you and your opponent have the same exact rules & dice). (4) Write an inversion algorithm that generates Y from U(0,1)