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Probability Theory

Following "A concise Course in Statistical Inference", I will start summarizing the main ideas.

Data analysis, pattern recognition, machine learning, data mining are general terms that we have seen a lot, which indeed refer to special cases of statistical inference. Particular problems are classification, prediction, clustering, estimation.

- In Probability, we study: Given a data generating process, what are the properties of the outcome?
- In Statistical Inference, we study: Given the outcomes, what can we say about the process that generated the data?

This first entry will devote for "Probability".

Probability theory, or probability distribution/density is a function that describes the probability of a random variable taking certain value. There are two kinds:

- Discrete probability distribution (or probability on finite sample spaces): characterized by a probability mass function
uniform probability distribution: if the sample space is finite and each outcome is equally likely.

- Continuous probability distribution, i.e., a distribution of a continuous random variable X, is a probability distribution that has a probability density function. For example: normal, uniform, chi-squared distribution.
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