Pages in Category Mathematics

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 …

**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) …

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 …

**[[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% …

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 …

**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 …

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 …

**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 …

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]] …

**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 …

**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 …

**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 …

**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 …

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 …

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

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Categories: Mathematics

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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

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Categories: Mathematics

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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 …

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Categories: Mathematics Systems Theory

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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

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Categories: Mathematics Software

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