Rest of 7.1 due on 11/19

Difficult
In Example (17), for x=0, f(x) = 0. But then the book implies you could set f(x) = lambda/2 because it doesn't matter. Why does it not matter? Why is that point "exceptional?" Also, I thought the later examples in the section were a bit difficult to follow. I think I got confused with the notation and all the Greek letters. I was able to (somewhat) follow up to the Normal Density example. After that, I was very confused.
Reflective
The book says that there are continuous random variables that do not have a density. What would these random variables look like? It must be something with a non-differentiable distribution function F, but I'm curious to see an example.