Hints and/or comments about Problem 21

• Be sure to note that X has a mean of 0 and a variance of 0.1. (Don't mistake the comma between the mean and variance for a digit, and note that the 2nd number is the variance and not the standard deviation.)
• While parts (a) and (c) can be done the old-fashioned way, with pencil and paper (or pen and paper for the daredevils amongst you), I think you'll find that part (b) is best done by making use of something like Maple or Mathematica (or I guess anything that can do numerical integration). (While you have your software at hand to do part (b), you may also want to use it for part (c).)
• Note that part (a) doesn't really require any heavy-duty calculus --- it can be easily solved using elementary probability. (Setting the probability of an event involving X equal to 0.5, convert to an equivalent event involving Y = e^X to determine the median of Y.)