Dice distributions

This is a bonus assignment so these points have not been factored into the grading scale. Directions for completing these tasks are purposely not given for this reason. Help screens and search engines may be able to help with the tasks below.

"Crazy dice" is a mathematical problem were dice are relabeled to provide the same probability distribution as a pair of fair 6-sided dice. See Sicherman dice for an example.

Task

Label a 4-sided die and a 9-sided die so that the sums of these dice have the same probability distribution as the sums of standard 2d6.

Provide sufficient evidence that your dice labels provide the correct distribution, i.e.,

Scoring