(New page: {| |- ! style="background: rgb(228, 188, 126) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initia...)
 
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! style="background: rgb(228, 188, 126) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; font-size: 110%;" colspan="2" | Taylor Series
 
! style="background: rgb(228, 188, 126) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial; font-size: 110%;" colspan="2" | Taylor Series
 
|-
 
|-
−
! style="background: rgb(238, 238, 238) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;" colspan="2" |  Taylor series of functions of single variable
+
! style="background: rgb(238, 238, 238) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;" colspan="2" |  Taylor series of Single Variable Functions
 
|-
 
|-
 
| align="right" style="padding-right: 1em;" | The complement of an event A (i.e. the event A not occurring)  
 
| align="right" style="padding-right: 1em;" | The complement of an event A (i.e. the event A not occurring)  
 
| <math>\,P(A^c) = 1 - P(A)\,</math>
 
| <math>\,P(A^c) = 1 - P(A)\,</math>
 
|-
 
|-
−
! style="background: rgb(238, 238, 238) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;" colspan="2" |  tylor series of functions of two variables
+
! style="background: rgb(238, 238, 238) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;" colspan="2" |  Binomial Series
 
|-
 
|-
−
| align="right" style="padding-right: 1em;" | Uniform random variable over (a,b)
+
| align="right" style="padding-right: 1em;" | The complement of an event A (i.e. the event A not occurring)  
−
| <math>\,E[X] = \frac{a+b}{2},\ \ Var(X) = \frac{(b-a)^2}{12}\,</math>  
+
| <math>\,P(A^c) = 1 - P(A)\,</math>
 
|-
 
|-
−
| align="right" style="padding-right: 1em;" | Gaussian random variable with parameter <math>\mu \mbox{ and } \sigma^2</math>
+
 
−
| <math>\,E[X] = \mu,\ \ Var(X) = \sigma^2\,</math>  
+
! style="background: rgb(238, 238, 238) none ! style="background: rgb(238, 238, 238) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;" colspan="2" |  Series Expansion of Exponential functions and Logarithms
 +
|-
 +
| align="right" style="padding-right: 1em;" | The complement of an event A (i.e. the event A not occurring)
 +
| <math>\,P(A^c) = 1 - P(A)\,</math>
 +
|-
 +
! style="background: rgb(238, 238, 238) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;" colspan="2" |  Series Expansion of Circular functions
 +
|-
 +
| align="right" style="padding-right: 1em;" | The complement of an event A (i.e. the event A not occurring)
 +
| <math>\,P(A^c) = 1 - P(A)\,</math>
 +
|-
 +
! style="background: rgb(238, 238, 238) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;" colspan="2" |  Series Expansion of Hyperbolic functions
 +
|-
 +
| align="right" style="padding-right: 1em;" | The complement of an event A (i.e. the event A not occurring)
 +
| <math>\,P(A^c) = 1 - P(A)\,</math>
 +
|-
 +
! style="background: rgb(238, 238, 238) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;" colspan="2" |  Various Series
 +
|-
 +
| align="right" style="padding-right: 1em;" | The complement of an event A (i.e. the event A not occurring)
 +
| <math>\,P(A^c) = 1 - P(A)\,</math>
 +
|-
 +
! style="background: rgb(238, 238, 238) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;" colspan="2" |  Series of Reciprocal Power Series
 +
|-
 +
| align="right" style="padding-right: 1em;" | The complement of an event A (i.e. the event A not occurring)
 +
| <math>\,P(A^c) = 1 - P(A)\,</math>
 +
|-
 +
! style="background: rgb(238, 238, 238) none repeat scroll 0% 0%; -moz-background-clip: -moz-initial; -moz-background-origin: -moz-initial; -moz-background-inline-policy: -moz-initial;" colspan="2" |  Taylor Series of Two Variables function
 +
|-
 +
| align="right" style="padding-right: 1em;" | The complement of an event A (i.e. the event A not occurring)
 +
| <math>\,P(A^c) = 1 - P(A)\,</math>
 
|-
 
|-
−
| align="right" style="padding-right: 1em;" | Exponential random variable with parameter <math>\lambda</math>
+
 
−
| <math>\,E[X] = \frac{1}{\lambda},\ \ Var(X) = \frac{1}{\lambda^2}\,</math>
+
 
|}
 
|}
  

Revision as of 14:06, 22 November 2010

Taylor Series
Taylor series of Single Variable Functions
The complement of an event A (i.e. the event A not occurring) $ \,P(A^c) = 1 - P(A)\, $
Binomial Series
The complement of an event A (i.e. the event A not occurring) $ \,P(A^c) = 1 - P(A)\, $
Series Expansion of Exponential functions and Logarithms
The complement of an event A (i.e. the event A not occurring) $ \,P(A^c) = 1 - P(A)\, $
Series Expansion of Circular functions
The complement of an event A (i.e. the event A not occurring) $ \,P(A^c) = 1 - P(A)\, $
Series Expansion of Hyperbolic functions
The complement of an event A (i.e. the event A not occurring) $ \,P(A^c) = 1 - P(A)\, $
Various Series
The complement of an event A (i.e. the event A not occurring) $ \,P(A^c) = 1 - P(A)\, $
Series of Reciprocal Power Series
The complement of an event A (i.e. the event A not occurring) $ \,P(A^c) = 1 - P(A)\, $
Taylor Series of Two Variables function
The complement of an event A (i.e. the event A not occurring) $ \,P(A^c) = 1 - P(A)\, $

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Alumni Liaison

Ph.D. on Applied Mathematics in Aug 2007. Involved on applications of image super-resolution to electron microscopy

Francisco Blanco-Silva