7.2 due 11/21

Difficult
In Example (2), I'm a little confused about why F(y) is non-zero for y <= 0 and then f(y) is non-zero for y>0. Why did the values of y switch? Also, the book says the derivative does not exist at y=0. I may be out of practice on derivatives, but I thought the derivative at y=0 was 0. Also, in the step function example, I don't quite see how FS(x) >= FX(x). I'm also having trouble understanding how an integer-valued random variable is an approximation of a continuous random variable.
Reflective
This section on functions of random variables is very similar to what we covered in section 5.4 - sums and products of random variables. Only now, we're dealing with more complicated functions, such as logs or exponents. I thought the examples on inverse functions were helpful since the ideas are kind of easy to grasp, but not so obvious mathematically.