The material is based largely on the following references:
The notes are divided into (roughly) one week worth of material (two 75-minute lectures):
. Generally speaking, the uniform probability measure on [a, b] can be defined as [3]:
A probability measure P on F is a real-valued function P on F with three properties [2]:Where:[1] Probability. arizona.
Probability measures have applications in diverse fields, from physics to finance and biology.
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[3] Probabilities. g.
The conditional probability based on the intersection of events defined as:
Probability measures are distinct from the more general notion of fuzzy measures in which there is no requirement that the fuzzy values sum up to
1
,
{\displaystyle 1,}
and the additive property is replaced by an order relation based on set inclusion. edu/~tgk/464_10/chap1_8_26. ininininAboutHelpTermsPrivacyMasters degree student in financial mathematics @ Masaryk university | Bc.
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The notes were used for two semester courses
at UW-Madison
(Spring 2018,
Fall 2013)
and two quarter courses at
UCLA
(Winter 2012,
Winter 2011,
Fall 2010,
Winter 2010). Retrieved March 11, 2021 from: https://www.
Market measures which assign probabilities to financial market spaces based on actual market movements are examples of probability measures which are of interest in mathematical finance; for example, in the pricing of financial derivatives.
The requirements for a function
{\displaystyle \mu }
to be a probability measure on a probability space are that:
For example, given three elements 1, 2 and 3 with probabilities
1
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/
4
,
1
/
4
{\displaystyle 1/4,1/4}
and
/
2
,
{\displaystyle 1/2,}
the value assigned to
{
1
,
3
}
{\displaystyle \{1,3\}}
is
1
/
4
+
1
/
2
=
3
/
4
,
{\displaystyle 1/4+1/2=3/4,}
as in the diagram on the right. .