A game is set where you roll a dice and your payo is equal to the number you roll. Before you participate you want to check some things.. (Show the calculations or use an argument)
1. What is your expected payo of the game?
2. What is the variance of the payo of the game?
3. What is the downside variance of the payo of the game (with respect to the mean)?
4. What is the Expected Shortfall at the 20% level?