Difference between revisions of "Statistics notes - on random variables, distributions, probability"

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==A few distributions==
 
==A few distributions==
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===Binomial distribution===
 
===Binomial distribution===
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Note that guassian and poisson (and others) can be extrapolated from this one.
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Note that  
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* since such a two-outcome event can be called a Bernoulli random variable, you can say that a binomial distribution is the sum of many independent such outcomes
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:: more precisely, that a binomial random variable is the sum of independent (but identically distributed) Bernoulli random variables. {{verify}}
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* there's also Bernoulli ''distributions''.
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: all Bernoulli distributions are binomial distributions, though most binomial distributions are not Bernoulli distributions.
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* gaussian and Poisson (and some others) can be extrapolated from binomial
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https://en.wikipedia.org/wiki/Binomial_distribution
 
https://en.wikipedia.org/wiki/Binomial_distribution
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https://math.stackexchange.com/questions/838107/what-is-the-difference-and-relationship-between-the-binomial-and-bernoulli-distr
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====Bernoulli Distribution====
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Basically binomial
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Revision as of 18:43, 4 July 2020

This is more for overview of my own than for teaching or exercise.

Overview of the areas

Arithmetic · 'elementary mathematics' and similar concepts
Set theory, Category theory
Geometry and its relatives · Topology
Elementary algebra - Linear algebra - Abstract algebra
Calculus and analysis
Logic
Semi-sorted
 : Information theory · Number theory · Decision theory, game theory · Recreational mathematics · Dynamical systems · Unsorted or hard to sort


Math on data:

  • Statistics as a field
some introduction · areas of statistics
types of data · on random variables, distributions
Virtues and shortcomings of...
on sampling · probability
glossary · references, unsorted
Footnotes on various analyses

Other data analysis, data summarization, learning

Regression · Classification, clustering, decisions · dimensionality reduction · Optimization theory, control theory
Connectionism, neural nets · Evolutionary computing



This article/section is a stub — probably a pile of half-sorted notes, is not well-checked so may have incorrect bits. (Feel free to ignore, fix, or tell me)

Dependent versus independent

Random variables, distributions

Probability function(/distribution)

Probability mass function (discrete)

Probability density functions (continuous)

Cumulative distribution function

Expected value

A few distributions

Binomial distribution

Poisson distribution

Gaussian/Normal distribution