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Pages in Category Mathematics

Bayes Theorem in Genetic Counseling

The picture shows a pedigree (as good as the dot software allows) of a family with a recessive x-linked disorder. The mutated X-chromosome is symbolized by the small letter x ...

Tags: Genetics Statistics


Categories: Mathematics


Bayes' theorem of probability

**Derivation of the [[http://en.wikipedia.org/wiki/Bayes%27_theorem|Bayes' theorem]]** can be made by the [[../ProbabilityProductRule|multiplication rule of probability]] and some algebra. <>P(A \cap B) = P(A) \cdot P(B \mid A))<> and <>P(A \cap B) ...

Tags: Statistics


Categories: Mathematics


Binomial distribution

Though this article tackles **[[http://en.wikipedia.org/wiki/Binomial_distribution|binomial distribution]]**, a type of [[../DiscreteProbabilityDistribution|discrete probability distribution]], it is rather focused on practical questions how to use [[http://matplotlib.org|matplotlib]] to construct such distributions. [[http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.binom.html|Numpy]] offers four ...

Tags: Statistics


Categories: Mathematics Software


Condorcet's jury theorem

**[[http://en.wikipedia.org/wiki/Condorcet's_jury_theorem|Condorcet's jury theorem]]** states that given two alternative decision of which one is correct. If the average probability of voters to arrive at the correct decision is more than 50% ...

Tags: Society Theory


Categories: Mathematics


Discrete probability distribution

By definition a **discrete probability distribution** exists if the following two requirements are met. * It exists a set of random variables <>x_i \: i=\{1,2,2,...\}<> and each of these variables ...

Tags: Statistics


Categories: Mathematics


Epigenetic landscape

**Epigenetic landscape** is a model introduced by [[../ConradHalWaddington|Conrad Hal Waddington]] that tries to explain the development into different directions depending on environmental or epigenetic factors. The model is a 3D ...

Tags: Control EvoDevo Evolution Genetics


Categories: Biology Mathematics


Fisher's fife-table mistakes

When reading about mathematical models of evolution you will probably inevitably bump into //The Genetical Theory Of Natural Selection//<>1<>. This book praised by many authors as the fundamental work ...

Tags: Genetics Society Statistics Theory


Categories: Mathematics


Injective and surjective functions

**Injectiveness** and **Surjectiveness** describe the mapping structure of functions as demonstrated by the following picture. <> digraph { ranksep=.1; size = "7.5,7.5"; rankdir=TB; subgraph cluster0{ color="red" label = "injective and ...

Tags: Functional Analysis


Categories: Mathematics


Poisson Distribution

Though this article tackles **[[http://en.wikipedia.org/wiki/Poisson_distribution|Poisson distribution]]**, a type of [[../DiscreteProbabilityDistribution|discrete probability distribution]], it is rather focused on practical questions how to use [[http://matplotlib.org|matplotlib]] to construct graphs of that distribution. [[http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.poisson.html|Numpy]] ...

Tags: Software Statistics


Categories: Mathematics Software


Probability density function

**Probability density function** (pdf) of a continuous random variable X is a function that satisfies the following requirements. <>f(x) \ge 0 \;\text{for all}\; x \in \Re <> <>\int_\Re f(x)dx<> If ...

Tags: Theory


Categories: Mathematics


Probability mass function

**Probability mass function** (pmf) of a discontinuous random variable X is a function that satisfies the following requirements. <>p_i \ge 0 \;\text{for all}\; i=1,2,3,..., <> <>\sum\limits_{i=1}^\infty p_i = 1<> with ...

Tags: Theory


Categories: Mathematics


Product rule of probability

Synonyms: Multiplication rule of probability

**Product rule of probability** applies to the coincidence of two events (A and B)(<>A \land B<>). In set theory symbols this is equivalent to the event C the intersection of ...

Tags: Statistics


Categories: Mathematics


Sum rule of probability

Synonyms: Addition rule of probability

**Sum rule of probability** describes the probability of the combination of two events (A **or** B) (<>A \lor B<>). In set theory symbols this is equivalent to the event C ...

Tags: Statistics


Categories: Mathematics


Venn Diagrams with Python Matplotlib and Django

Unfortunately there is no proper tool in python to visualize set operations and relations, neither in maplotlib nor in graphviz. The closest solution that I found was a Venn diagram ...

Tags: Software


Categories: Mathematics Software


Random walk

This page mainly shows a random walk example implemented in python with numpy and pylab. The theory behind random walk [[http://en.wikipedia.org/wiki/Random_walk|can be learned from Wikipedia]]. <Theory


Categories: Mathematics


Space of real numbers

<> graph "" { # null set # n000 ; # n000 [label="0"] ; size="12,12"; resolution=72; bgcolor="#FFFFFF"; # first set n001 ; n001 [label="1"] ; n001 -- n011 ; n011 ...

Tags: Theory


Categories: Mathematics


Set Operations

This page demonstrates fundamental set operatons and the corresponding Venn diagramms as reference. The resulting set is shown in red. == Union <>A \cup B<> <> def ...

Tags:


Categories: Mathematics Systems Theory


Slider Widget in Django

A slider widget can be implemented in Django. **Update:** Slider widget is no longer supported as [[../SageSingleCellServerMacro|I implemented sage cells]] for that purpose which offers much more functionality (including sliders). ...

Tags: Software


Categories: Mathematics Software


 
   

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