1. An online gambling platform, TrueGame, provides a very simple gambling to its users, 'Rolling a dice.' As you all know, there are six possible outcomes: 1, 2, 3, 4, 5, and 6 . In each game, you need to bet $1. If the outcome is 1 , you will receive $5 (\$4 plus the $1 you bet) and nothing if the outcome is not 1 . (a) (2 points) What are the expected value and standard deviation of TrueGame's profit in each bet? (b) (3 points) Suppose 1 million similar bets are placed in a typical month. (1) What is the standard deviation of TrueGame's average profits per dollar bet each month? (2) What is the standard deviation of monthly profit