RPythonBook/09-Probability.Rmd at master · medmatix/RPythonBook · GitHub

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# Using Probability Distributions with R and Python

This chapter will not be an exhaustive handling of mathematical probability. Refer for more depth to any introductory text on probability^30^. Context is provided, somewhat, here in the following overview of the domain of probability. I suspect all have had a course in probability and statistics if you have been usinf R and this few paragraphs can be skipped over. Those with no probability of statistics would be well served to atleast skim Kerns^32^ book along with the examples. The Chapter on probability in Grus^9p69^ is also recommended. See the Resources in [Appendix 4.]()


An outcome one of the possible results in an experiment^29^. Any process of observation or measurement is called an experiment. An event is an outcome or defined collection of outcomes of a random experiment.

A set of outcomes of an experiment forms a sample space. A population is the set of **all possible** events of some phenomenon.

A random variable is one such that it's possible values are outcomes of a random process^27p92^. More formally, a function that maps (connects) outcomes of unpredictable processes to numerical quantities defines a randon variable.

\index{probability}
Probability, P is "a number that represents how likely it is that a particular thing will happen"^29^, usually expressed as the fractional occurance of a result divided by this result and all such other  possible results of a phenomenon. Frequently a function may obtain which expresses the fractional occurance of a specific event obtaining from the population of all possible outcomes, as stated above.

A probability space consists of three parts^31^:

> 1.   A sample space, Ω  which is the set of all possible outcomes.
 2.    A set of events,  F  where each event is a set containing zero or more outcomes.
 3.    The assignment of probabilities to the events; that is, a function P from events to probabilities.
\index{probability distribution}
A probability distribution is a function mapping to a set of possible outcomes. The set may be arbitrarily defined or otherwise, like set of fractional values, whole number values decimal values and so on.

Each probability distribution has a defining characteristic which determine's it's application to a sample of data. It may represent a collection of descrete outcomes, such as the set of possitive integers, or it may represent a continuous line of possible outcomes, such as the set of real numbers.It may be a subset of the set Q of rational numbers and therfore representative of proportions of a whole. etc.


\index{Grus}


## Basic Probability Issues

With the above in the far back of our mind, we will basically consider matters of probability using R and Python. An approchable source for learning probability and statistics with R^32^ will provide some code examples to illustrate. As will Grus^9^ with python.

### Drawing from a Deck Cards as a Population of Outcomes


### R Scripting


### Python Scripting


## Using the Distrbutions

\index{probability distribution}

### R Scripting


### Python Scripting


## Other Libraries with Probability and Statistical Packages

### R Scripting


### Python Scripting