Assignment:
One evening, Fyodor decides to play 10 games of roulette, betting $100 on black each time (this bet wins $100 with probability 18/38, and otherwise loses $100).
(i) What is the expected value and standard deviation of his total winnings?
(ii) Find the exact chance (i.e., not using a normal approximation) that he loses $400 or more over the course of the evening.
Provide complete and step by step solution for the question and show calculations and use formulas.