Imagine you're running a casino and introducing a new game. The game involves rolling a fair six-sided die. Each player pays $10 to play. If the die shows a 1 or 2, the player wins $20. If it shows a 3 or 4, the player wins $10. If it shows a 5 or 6, the player loses. Discuss how you would calculate the expected value, standard deviation, and variance of this game. How might these statistical measures help you understand the potential profitability and risk associated with offering this game in your casino