Problem 4 [20 pts]: The Wheaton Curse So here's a real spooky tale. Wil Wheaton(he/him) is a man with an incredible curse: he always rolls really badly on dice during table top games. 1 So let's look at Wil's curse in a little more detail. Let's assume we are playing a game where Wil needs to roll a high number on a 20-sided die. A 20-sided die has can roll any integer between 1 and 20. Experts have shown in this scenario, there is a 2,3 chance to roll any integer between 1 and 6 on the die and a % chance to roll any integer between 7 and 20. Within that 23 chance, the integers between 1 and 6 show are equally likely to appear. This is the same with the % chance at the integers between 7 and 20. i. Calculate the expected value of Wil rolling a 20-sided die 5 times in a row. (Optionally marvel at the effects of his curse!) ii. The Wheaton curse is transferable to other dice. When cursed, every die acts as if Wil is rolling them, retaining the probabilities experts have found earlier. You have obtained a die that might have the Wheaten curse. At the moment, this die is equally likely to be cursed or fair. You (with gloves) roll the die 5 times and get the following results in order: 1, 4, 2, 3, 1. In your heart of hearts, you know it must be cursed, but you must conrm. Calculate and compare the probabilities of getting the outcome given the die is fair versus the die is cursed. Is it more likely the die has the Wheaton curse or not