Problem 7: Fair Coin Gambling (a) (10 points) A person pays $1 to play the following game. The person tosses a fair coin four times. If no heads occur, the person pays an additional $2, if one head occurs, the person pays additional $1, if two heads occur, the person just loses the initial dollar, if three heads occur, the person wins $3, and if four heads occur, the person wins $4. What is the person's expected loss or gain