Distribution functions,
binomial, geometric,
hypergeometric, and Poisson distributions.
The other topics covered are uniform,
exponential, normal,
gamma and beta distributions;
conditional probability;
Bayes theorem; joint distributions;
Chebyshev inequality; law of large numbers; and central limit theorem.
Most simply stated, probability is the study of randomness. Randomness is of course everywhere around us—this statement surely needs no justification! One of the remarkable aspects of this subject is that it touches almost every area of the natural sciences, engineering, social sciences, and even pure mathematics. The following random examples are only a drop in the bucket.
• Electrical engineering: noise is the universal bane of accurate transmission of information. The effect of random noise must be well understood in order to design reliable communication protocols that you use on a daily basis in your cell phones. The modelling of data, such as English text, using random models is a key ingredient in many data compression schemes.
• Statistics and machine learning: random models form the foundation for almost all of data science. The random nature of data must be well understood in order to draw reliable conclusions from large data sets.
• Pure mathematics: probability theory is a mathematical field in its own right, but is also widely used in many problems throughout pure mathematics in areas such as combinatorics, analysis, and number theory.