4.3 due on 10/19

Difficult
I'm not sure how we can assign positive infinity or negative infinity to E(X) if by definition, E(X) must be finite. I'm also not sure what the purpose is of the real-valued function g(.). Is the domain of g the actual random variable or is it the range of X? What does it mean to to find the expected value of X^2? What is the definition of a moment? I'm also very confused by the Coupons example, as well as others in this section. I think the reason I'm having so much trouble following these examples is because I still don't completely understand the previous section.
Reflective
The idea of expectation makes a lot of sense to me. Since more weight is given to a particular value of X based on its probability, the greater the probability, the more likely it is that value occurs. Pictorially it's like a graph, where the value with the highest expectation is where the area below is the largest.