CDS 110b: Stochastic Systems - Revision history

Murray at 03:28, 2 March 2008

2008-03-02T03:28:14Z

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	{{cds110b-wi08\|prev=State Estimation\|next=Kalman ~~Fitlers~~}}		{{cds110b-wi08 lecture\|prev=State Estimation\|next=Kalman Filters}}
	This set of lectures presents an overview of random processes and stochastic systems. We begin with a short review of continuous random variables and then consider random processes and linear stochastic systems. Basic concepts include probability density functions (pdfs), joint probability, covariance, correlation and stochastic response. __NOTOC__		This set of lectures presents an overview of random processes and stochastic systems. We begin with a short review of continuous random variables and then consider random processes and linear stochastic systems. Basic concepts include probability density functions (pdfs), joint probability, covariance, correlation and stochastic response. __NOTOC__

2008-03-02T03:28:05Z

← Older revision		Revision as of 03:28, 2 March 2008
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	{{cds110b-wi08}}		{{cds110b-wi08\|prev=State Estimation\|next=Kalman Fitlers}}
	This set of lectures presents an overview of random processes and stochastic systems. We begin with a short review of continuous random variables and then consider random processes and linear stochastic systems. Basic concepts include probability density functions (pdfs), joint probability, covariance, correlation and stochastic response. __NOTOC__		This set of lectures presents an overview of random processes and stochastic systems. We begin with a short review of continuous random variables and then consider random processes and linear stochastic systems. Basic concepts include probability density functions (pdfs), joint probability, covariance, correlation and stochastic response. __NOTOC__

2008-02-18T00:27:21Z

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 </amsmath></center>
 If we assume that <math>\mu_X = \mu_Y = 0</math> then the result follows.  (Alternatively, compute <math>E\{(X - \mu_X) (Y - \mu_Y)\}</math>
 </blockquote>

2008-02-18T00:16:39Z

← Older revision		Revision as of 00:16, 18 February 2008
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	* {{cds110b-wi07 pdfs\|stochastic.pdf\|Lecture notes: Stochastic Systems}}		* {{cds110b-wi07 pdfs\|stochastic.pdf\|Lecture notes: Stochastic Systems}}
	* {{cds110b-wi08 pdfs ~~placeholder~~\|hw5.pdf\|HW #5}} (due Wed, 20 Feb)		* {{cds110b-wi08 pdfs\|hw5.pdf\|HW #5}} (due Wed, 20 Feb)

	== References and Further Reading ==		== References and Further Reading ==

2008-02-15T17:02:35Z

References and Further Reading

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	== References and Further Reading ==		== References and Further Reading ==
	* R. M. Murray, ''Optimization-Based Control''. Preprint, 2008: {{obc08 pdfs\|~~stochastic_13Feb08~~.pdf\|Chapter 4 - Stochastic Systems}}		* R. M. Murray, ''Optimization-Based Control''. Preprint, 2008: {{obc08 pdfs\|stochastic_15Feb08.pdf\|Chapter 4 - Stochastic Systems}}
	* Hoel, Port and Stone, Introduction to Probability Theory - this is a good reference for basic definitions of random variables		* Hoel, Port and Stone, Introduction to Probability Theory - this is a good reference for basic definitions of random variables
	* Apostol II, Chapter 14 - another reference for basic definitions in probability and random variables		* Apostol II, Chapter 14 - another reference for basic definitions in probability and random variables

2008-02-13T23:29:34Z

← Older revision		Revision as of 23:29, 13 February 2008
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	== References and Further Reading ==		== References and Further Reading ==
	* R. M. Murray, ''Optimization-Based Control''. Preprint, 2008: {{obc08 pdfs\|~~stochastic_12Feb08~~.pdf\|Chapter 4 - Stochastic Systems}}		* R. M. Murray, ''Optimization-Based Control''. Preprint, 2008: {{obc08 pdfs\|stochastic_13Feb08.pdf\|Chapter 4 - Stochastic Systems}}
	* Hoel, Port and Stone, Introduction to Probability Theory - this is a good reference for basic definitions of random variables		* Hoel, Port and Stone, Introduction to Probability Theory - this is a good reference for basic definitions of random variables
	* Apostol II, Chapter 14 - another reference for basic definitions in probability and random variables		* Apostol II, Chapter 14 - another reference for basic definitions in probability and random variables

2008-02-13T06:56:45Z

← Older revision		Revision as of 06:56, 13 February 2008
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	== References and Further Reading ==		== References and Further Reading ==
	* R. M. Murray, ''Optimization-Based Control''. Preprint, 2008: {{obc08 pdfs\|~~stochastic_11Feb08~~.pdf\|Chapter 4 - Stochastic Systems}}		* R. M. Murray, ''Optimization-Based Control''. Preprint, 2008: {{obc08 pdfs\|stochastic_12Feb08.pdf\|Chapter 4 - Stochastic Systems}}
	* Hoel, Port and Stone, Introduction to Probability Theory - this is a good reference for basic definitions of random variables		* Hoel, Port and Stone, Introduction to Probability Theory - this is a good reference for basic definitions of random variables
	* Apostol II, Chapter 14 - another reference for basic definitions in probability and random variables		* Apostol II, Chapter 14 - another reference for basic definitions in probability and random variables

2008-02-12T04:33:09Z

← Older revision		Revision as of 04:33, 12 February 2008
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	* {{cds110b-wi07 pdfs\|stochastic.pdf\|Lecture notes: Stochastic Systems}}		* {{cds110b-wi07 pdfs\|stochastic.pdf\|Lecture notes: Stochastic Systems}}
	* {{cds110b-wi08 pdfs placeholder\|hw5.pdf\|HW 52}} (due Wed, 20 Feb)		* {{cds110b-wi08 pdfs placeholder\|hw5.pdf\|HW #5}} (due Wed, 20 Feb)

	== References and Further Reading ==		== References and Further Reading ==

2008-02-12T01:45:44Z

Frequently Asked Questions

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	'''Q (2008): Why does E{X Y} = 0 if two random variables are independent'''		'''Q (2008): Why does E{X Y} = 0 if two random variables are independent'''
	<~~blockqoute~~>		<blockquote>
	By definition, we have that		By definition, we have that
	<center><amsmath>		<center><amsmath>
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	</amsmath></center>		</amsmath></center>
	If we assume that <math>\mu_X = \mu_Y = 0</math> then the result follows. (Alternatively, compute <math>E\{(X - \mu_X) (Y - \mu_Y)\}</math>		If we assume that <math>\mu_X = \mu_Y = 0</math> then the result follows. (Alternatively, compute <math>E\{(X - \mu_X) (Y - \mu_Y)\}</math>
	</~~blockqoute~~>		</blockquote>

	'''Q (2006): Can you explain the jump from pdfs to correlations in more detail?'''		'''Q (2006): Can you explain the jump from pdfs to correlations in more detail?'''

2008-02-12T01:45:07Z

Frequently Asked Questions

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	</amsmath></center>		</amsmath></center>
	If we assume that <math>\mu_X = \mu_Y = 0</math> then the result follows. (Alternatively, compute <math>E\{(X - \mu_X) (Y - \mu_Y)\}</math>		If we assume that <math>\mu_X = \mu_Y = 0</math> then the result follows. (Alternatively, compute <math>E\{(X - \mu_X) (Y - \mu_Y)\}</math>
	~~</amsmath></center>~~

	</blockqoute>		</blockqoute>