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