Learning probability theory on the web
Learning probability theory on the web
Learning probability theory on the web
Probability and mathematical statistics are challenging subjects and students often find it difficult to find learning resources that cover this subject at the right level. This Articlesbase article explains how to use learning materials that are freely available on the Web to learn probability and mathematical statistics.
There are plenty of websites that can help a student approach probability theory and mathematical statistics at various levels of difficulty.
You can find below a brief description of the following websites:
1. The Lessons on Probability theory by G. Glosser (at MathGoodies)
2. The Lectures on Probability by M. Taboga (at StatLect)
3. The Probability Tutorials by N. Vaillant (at Probability.net)
The three websites above are listed in order of difficulty, starting from the easiest.
MathGoodies.com has a lot of fairly intuitive material on entry-level probability theory. This is excellent as a starting point, to quickly familiarize yourself with the basics of statistics and probability. If you think you are comfortable with the studying material at MathGoodies, you can proceed to more sophisticated levels (see below).
StatLect.com introduces the fundamentals of probability theory in a much more rigorous manner. StatLect discusses probability theory at an intermediate level, it contains a lot of details and uses more sophisticated mathematics (although not very sophisticated!). The numerous topics you can find at StatLect are carefully explained and you can find many step-by-step derivations of important results, solved exercises and examples. Furthermore, you can find multiple choice questions on probability theory to check your level of knowledge.
Probability.net contains very rigorous material, at a high level of mathematical sophistication (it makes intensive use of measure theory and functional analysis).
There are also many other places on the web where you can find learning materials about probability and mathematical statistics. For instance, there are lots of interesting videos on YouTube where probability and mathematical statistics are taught by teachers and university professors. After learning about a topic in one of the websites I mentioned above, you can write a list of the most important keywords you have encountered (e.g.: 'probability density function' or 'cumulative distribution function') and search for those keywords on YouTube. By doing so, you will probably find several videos that explain the term you have searched for.
However, bear in mind that solving exercises is the best way to acquire a sound knowledge of probability and statistics. The websites mentioned above (and StaLect in particular) contain a number of probability exercises with explained step-by-step solutions. For example, on StatLect you can find exercises on probability, conditional probability, independent events, random variables and random vectors, probability distributions, characteristic functions, indicator variables, conditionasl expectation, variance, covariance, probability density functions, the Riemann-Stieltjes integral and other advanced topics. All the exercises you find on StatLect are complemented by a step-by-step solution. The latter is not visible at first, but then you can click on a drop-down button to see the solution after you have tried to solve the exercise by yourself. Finally, on StatLect you can also find probability multiple choice questions, to test your knowledge in a quick way. The multiple choice tests are divided by subject and at the end of each multiple choice test you can see your score (how well you have done on that particular multiple choice test).
Have fun studying probability theory!
A Torrent of College Applications Odessa Ukraine National University Leadership University Learn About The Healing Power of the Mind - It Is Your Ultimate Tool for Life Polls Create A Collaborative Classroom University of Cambridge - The NO.1 of QS World University Rankings 2010 Harvard University - The NO.2 of QS World University Rankings 2010 Learn Spanish The Convenient Way How to live with Room Mates in college/university hostels? How to select college after matriculation? Yale University - The NO.3 of QS World University Rankings 2010 Enzootic Taeniasis in Lambs, a Case Study Oracle 1Z0-518 Practice Questions from Exampdf