# Is probability branch of maths or stats?

woundedtiger4
Hi all,

I was wondering if someone can tell me that is probability branch of mathematics or statistics. Wikipedia says that Probability Theory is branch of mathematics but in University Statistics department offers probability modules.
Also, is Statistics branch of mathematics, after all it deals with numbers. Am I wrong?

Nessdude14
Statistics is usually considered to be its own branch of science. However, statistics also refers to a branch of mathematics. It depends on the context you hear it in. If you hear it in your math class, they're probably referring to the mathematical methods of statistics.

Probability is another branch of mathematics which is often used as a tool in statistics. However, probability can be calculated without the use of the mathematical methods of statistics, and thus is not simply a subset of statistics.

The relationship between probability and statistics is somewhat analogous to the relationship between science and engineering.

Hey woundedtiger4.

Statistics concerns itself with the study of a function of a sample. A sample is considered a set of observations from some distribution (usually independent but not always) and the statistics is some function of that sample. For example the sample mean is just the average of all values of the sample.

Probability itself can be formulated in the language of measure theory and analysis can be used to deal with the definitions of convergence in similar ways to that of a normal function mappings.

All this measure theory and analysis is applied to what is called stochastic calculus to prove a lot the results for stochastic processes.

But although you can formulate probability spaces in the above way (using what is called a sigma-algebra), it's usually done in a way that is a lot more intuitive.

Usually we focus more on the context of how it applies in the real world which means not worrying about all the theoretical proofs using measure theory and analysis but instead looking at things in a practical manner.

The really basic foundations of probability are the Kolmogorov axioms which are based on set theory descriptions of probability.

You should check whether the math offering covers the sigma algebra approach and whether the non-math offering covers the standard topics like the axioms, definitions of PDF's, CDF's, MGF's, variance/covariance and things like the transformation theorems as well as exercises and assignments that focus on real problems dealing with tangible uncertainties as opposed to those involving proofs of analysis and measure theory.

woundedtiger4
thanks @ all for excellent replies