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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 [...]

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 [...]

To illustrate another similar example from last post, now supposed ALL the A-level Candidates met up in the town square. Prior to meeting up, they were all told by the head examiner that if [...]

Over the past two months, I’ve been reading up on Game Theory extensively. It has always been a subject of interest for me since undergraduate days. And I’m glad that I found time to read a bit [...]

Some of you will probably hear of this two terms and wonder what’s the difference. Both of them are a statistical approach/ inference method. Personally, I am a Bayesian and use more of [...]

During class, I occasionally mention to students that the calculus you learnt is deterministic and they go uh huh. So like what is non deterministic?! I’ll attempt to give some simple [...]