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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 Bayes' theorem can be made by the multiplication rule of probability and some algebra. and Subtracting these two equations leads: and some algebraic transformation yields the theorem

Tags: Statistics


Categories: Mathematics


Binomial distribution

Though this article tackles binomial distribution, a type of discrete probability distribution, it is rather focused on practical questions how to use matplotlib to construct such distributions. Numpy offers four ...

Tags: Statistics


Categories: Mathematics Software


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 ...

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 and each of these variables has a corresponding probability ...

Tags: Statistics


Categories: Mathematics


Epigenetic landscape

Epigenetic landscape is a model introduced by 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.

Tags: Functional Analysis


Categories: Mathematics


Poisson Distribution

Though this article tackles Poisson distribution, a type of discrete probability distribution, it is rather focused on practical questions how to use matplotlib to construct graphs of that distribution. 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. If the random variable X is discontinuous the probability mass function is ...

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. with being the probability of event . In case of a continuous random ...

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)(). In set theory symbols this is equivalent to the event C the intersection of events A ...

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) ().
In set theory symbols this is equivalent to the event C the union of ...

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 can be learned from Wikipedia.
def set_figure(fig):    
   import numpy ...

Tags: Theory


Categories: Mathematics


Space of real numbers

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
def set_figure(fig):    
   from matplotlib_venn import venn2

   ax=fig ...

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 I implemented sage cells for that purpose which offers much more functionality (including sliders ...

Tags: Software


Categories: Mathematics Software


 
   

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