Probability Theory is a beautiful subject. It might seem a bit obscure at first to some and if that's the case, don't despair and don't give up. You can also fire a few emails to me if you just can't get your head around it. Once you understand that, ultimately, probability is just a mathematical measure of uncertainty and once you start concentrating on understanding the phenomena rather than blindly applying formulas, you are on the path of becoming a successful thinking probabilist.
We may do only three supervisions, depending on progress and
- Problems 1-9 from Richard Gibbens' Problem Sheet.
- Problems 10-15 from Richard Gibbens' Problem Sheet.
- Show that for any discrete random variable that has a PGF, its
probability mass function p(k)
is given by p(k)
/ k!, where G(k)(z)
is the kth derivative of the PGF function G(z).
- Questions 1-3 from my Question list.
- Given a random variable X, either discrete or
continuous, we define M(t)
assuming this expectation exists. Show that the nth
moment of X, i.e. E[Xn],
in both discrete and continuous cases is given by E[Xn]
is the nth derivative of M(t).
For a discrete X, assume a probability mass function p(k). For
a continuous X, assume a continuous probability density
- Problems 5-9, 12, 13, 17, 19, 22 from my Question
- Questions 4, 10, 14, 16, 18, 21 from my Question
NOTE: These are non-trivial, don't start the work late.