4.6 Due on 4/10/2008

Difficult
In the solution of example (9), I am not sure why the Chebyshov's Inequality is used to solved this problem. Is it possible to use the other inequalities listed in this section to solve this problem? The Chebyshov's Inequality is used here, is it because the problem states that "X be a random variable such that var(X)=0"?

Reflective
In the solution of example (16), the differential calculus is used to prove that -logx is convex. That's the part that I think it's interesting, because differential calculus was the first or second class we've taken, and I think I will never use that again, but the differential calculus knowledge is actually requared here. So, reading this section remains me once again, that the materials in the field of mathematics are attached to each other.