Logarithm and Probability: Difference between pages

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1.
The study of chance providing an objective measure of uncertainty.


The mathematical function which is the inverse of "raising to the power of".


Usually abbreviated to "log".
Probabilities range between 1 (=100%) and 0 (=0%).


A probability of 100% means that an event is considered certain to occur.


'''Example'''
A probability of 0% means that an event is considered certain not to occur. 


Working with logarithms to the base 10:


log<sub>10</sub>(100) = 2
For example, flipping an unbiased coin, the probability of getting a head is often modelled as 50%.


And 10<sup>2</sup> = 100


This simple model of a coin flip assumes that the only two possibilities are a head or a tail.  Applying such simple models to financial situations, and treating financial outcomes as simple coin flips, may lead to errors resulting from:


 
#The coin landing on its edge 'more often than it's supposed to'.
More generally with logarithms to the base n:
#The underlying assumption of an unbiased coin not being a valid one. This kind of assumption is usually much too simple.
 
log<sub>n</sub>(x) = the power which, when 'n' is raised to it = x
 
 
'''Example'''
 
10<sup>(log<sub>10</sub>(x))</sup> = x
 
And, more generally, n<sup>(log<sub>n</sub>(x))</sup> = x
 
 
2.
 
The logarithm to the base 10.




== See also ==
== See also ==
* [[Natural logarithm]]
* [[Black swan]]
* [[Conditional probability]]
* [[Confidence interval]]
* [[Frequency distribution]]
* [[Mutually exclusive]]
* [[Poisson distribution]]

Revision as of 15:19, 8 June 2016

The study of chance providing an objective measure of uncertainty.


Probabilities range between 1 (=100%) and 0 (=0%).

A probability of 100% means that an event is considered certain to occur.

A probability of 0% means that an event is considered certain not to occur.


For example, flipping an unbiased coin, the probability of getting a head is often modelled as 50%.


This simple model of a coin flip assumes that the only two possibilities are a head or a tail. Applying such simple models to financial situations, and treating financial outcomes as simple coin flips, may lead to errors resulting from:

  1. The coin landing on its edge 'more often than it's supposed to'.
  2. The underlying assumption of an unbiased coin not being a valid one. This kind of assumption is usually much too simple.


See also

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