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Lets look at brownian motion now. And yes, its the same as what our high school teachers taught about the particles moving in random motion. Here, we attempt to give it a proper structure and [...]

So I understand that I lost many readers for the Sampling uploads.It is a bit difficult to the intensive use of notations and also the need for statistics knowledge. So here I’ll review a [...]

This is a rather important topics for anyone interested in doing Finance. Lets look at their definition first. A Martingale is a random process with respect to the information filtration and the [...]

Let be an n-dimensional vector of random variables. For all , the joint cumulative distribution function of X satisfies Clearly it is straightforward to generalise the previous definition to join [...]

In all these years of teaching, I realised that many JC students still do not know a handful of things. So I will list down a few random ones that I can recall off-hand, and of course expand a [...]

Here we look at an important concept that is an extension from Bayes Theorem, which we discussed briefly. The condition expectation identity says The condition variance identity says Here both [...]

We look at the definitions first. A continuous random variable, X, has a probability density function (PDF), if and for all events A The CDF and PDF are related by It is good to know that we have [...]

As usual, definitions first. The cumulative distribution function (CDF), of a random variable, X, is defined by A discrete random variable, X, has probability mass function (PMF), , if and for [...]

Happy 2016 to everyone! I’ve a really exciting news to share now with regards to H2 Mathematics. As I mentioned in a post before, I felt that the current H2 Mathematics can do some [...]

Some inquisitive students have asked me before, how the MF15 integration formulas come about. I thought I should share it too then. So we want to and yes, we know the formula can be plugged [...]