Congratulations for making it to the end of

week six of the MOOC and hence the end of the course.

I say the end, in fact,

I hope for you this is very much the beginning of

your career dealing with probability and statistics.

The whole purpose of this MOOC was just to give you a gentle introduction to

hopefully quite a broad or cross section of

themes ranging from simple probability distributions,

some descriptive statistics, the elements of statistical inference i.e.

point estimation, interval estimation,

hypothesis testing, and throughout week six,

we've been introducing you to a range of

further more advanced kinds of analytical models.

So to become proficient in quantitative work,

takes time, takes perseverance and effort.

Now, in a short MOOC such as this,

well of course one has to have realistic expectations about how much one can absorb.

However, I hope very much that this MOOC has piqued

your interest to pursue further quantitative courses.

So I'd like to just treat this as the course wrap up,

packed some words of wisdom,

some words of advice for you as hopefully you decide

to further your interests and studies in the quantitative world.

So, which areas should I perhaps suggest you focus on?

So this MOOC attempted to expose you to

a wide variety of different aspects of probability and statistics.

We've considered some theoretical aspects deriving some simple probability distributions.

A useful thing to do here after is to explore

the wide array of different probability distributions which exist out there.

Discrete distributions, continuous distributions,

in the mixed distributions with both discrete and continuous components.

We've dabbled with minor issues such as the mean and the variance but there's

a whole wealth of further characteristics of probability distributions to discover.

Indeed, our final look at Monte Carlo simulation,

we saw probability distributions there being used as inputs to these Monte Carlo models.

So an awareness and an appreciation for

the numerous probability distributions which exist out there,

would put you in very good stead if you wanted to

develop more of your abilities in Monte Carlo work.

As well as the statistics side is concerned,

we began with a simple descriptive statistics,

some data visualization, of course,

these are critical things to do with any empirical analysis.

You take those baby steps first of all,

you walk before you can run.

And indeed, whenever you come across a data set,

I want you exploring it at the descriptive level,

some simple graphical displays,

get a feel of the distributions of your variables,

calculate some simple descriptive statistics for them.

But I think going beyond that,

a worthwhile exercise is to explore more statistical inference.

Point estimation.

It's a very superficially i.e,

use a sample mean to estimate a population mean.

Clearly, point estimation is quite more involved than that.

Perhaps some recommendations for you are different kinds of point estimation techniques.

You might like to do some internet searches for things like

method of moments estimation, least squares estimation,

a staple used in regression analysis and very importantly,

something called maximum likelihood estimation.

Now these are some quite substantial techniques

which will take some time to fully master.

But I think it is worthwhile you persevering and indeed overcoming those barriers.

Because if you have a deep understanding of point estimation,

what we mean by an estimator,

the statistical properties of an estimator,

how we pick a desirable estimator,

then this will really allow you to gain

a deep understanding of those important areas of statistical inference i.e.

confidence intervals and of course, hypothesis testing.

We've merely scratched the surface giving you a few simple introductory examples.

So to freely utilize statistical inference techniques,

it's helpful if you can have a solid grounding in probability and distribution theory.

We mentioned p values.

Well, how do you actually calculate them?

What is the probability theory behind it?

Again, taking further courses in probability and

distribution theory will allow you to have

a deep understanding about why things are the way they are.

Of the week six topics,

we've introduced decision tree analysis. I love it.

Regression analysis. I love it.

Linear Programming. I love it.

And Monte Carlo simulation.

I really love it.

But these are by no means an exhaustive list of the types of analysis out there.

For example, time series data.

How do we deal with it?

How do we forecast the future?

Maybe you're trying to forecast a share price, an exchange rate,

the sales of your company.

Clearly not easy.

No one knows the future,

no one has this magic crystal ball but

we can at least come up with some predictions, some forecasts.

You want to perhaps decide how good,

how accurate these forecasts are.

That indeed involves creating and constructing various prediction and forecasting models.

So perhaps, you may wish to take further courses in time series and forecasting.

So there's a wealth of probability and statistics out there.

We are entering the era of big data, data science,

machine learning, you're going to hear about these terms more and more in the media.

So of course, it takes time, effort,

and perseverance to become fully proficient in these sorts of techniques.

But I guarantee you,

perhaps one of the few certainties in there I think we can add this to death and taxes.

I'll offer you this as another certainty in life,

that if you decide to invest a lot of time and

effort into becoming very good at probability and statistics,

I think the job prospects for you are very bright indeed.

So I called this MOOC probability and statistics,

to p or not to p. So

perhaps an appropriate closing remark is to reconsider this question of,

to p or not to p. Now this was my PhD thesis title,

the p there did refer to p value.

I think we can extend it more generally,

to think now a p about probability.

So, should we take a probabilistic approach to

life or should we not take a probabilistic approach to life?

Well inevitably, I'm biased but I'd like to think I'm right

too in that we are living in a world of uncertainty.

We always have we always will.

We continue to have to make decisions in the present with

these unknown uncertain future outcomes.

So the best we can do is to try and come up with

a probabilistic assessment of the future and

take what we deem to be the optimal decisions based

on the information we have available to us here and now.

I don't promise you success every single time.

That Monty whole problem you did there,

hopefully the right strategy of switching

door but in our iteration of the game, you lost.

Well, that was just bad luck.

We all experience bad luck but we can also experience good luck as well.

But if we have a proper sense and understanding about risk, uncertainty,

and really can interpret probabilities and really know what these mean,

this will aid our decision making a great deal.

And one hopes that if the whole of humanity was enlightened

about probability and statistics,

and I'd like to think we all generally go on and make a better decisions and hopefully,

we can make the world a better place.

Well, that's an aspiration, will it be met?

Who knows. We live in this world of uncertainty.

Time will tell.

So thank you very much for joining me in this MOOC and I wish you all the very

best in your future studies of probability and statistics. Goodbye.