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- 12:19, 17 November 2010 (diff | hist) . . (+563) . . ECE 600 General Concepts of Stochastic Processes Definitions
- 12:12, 17 November 2010 (diff | hist) . . (+13,550) . . N ECE 600 General Concepts of Stochastic Processes Definitions (New page: 3.1 Definitions Stochastic process The idea of a stochastic process is a straightforward extension of that of random variable. Instead of mapping each <math>\omega\in\mathcal{S}</math> ...)
- 11:42, 17 November 2010 (diff | hist) . . (+1) . . ECE 600 General Concepts of Stochastic Processes
- 11:42, 17 November 2010 (diff | hist) . . (+52) . . ECE 600 General Concepts of Stochastic Processes
- 11:41, 17 November 2010 (diff | hist) . . (+3) . . ECE 600 General Concepts of Stochastic Processes
- 11:41, 17 November 2010 (diff | hist) . . (+282) . . N ECE 600 General Concepts of Stochastic Processes (New page: *[ECE 600 General Concepts of Stochastic Processes Definitions|Definitions]] *[ECE 600 General Concepts of Stochastic Processes Systems with Stochastic Inputs|Systems with Stochastic Input...)
- 11:37, 17 November 2010 (diff | hist) . . (+1,580) . . N ECE 600 Random Sum (New page: 2.6 Random Sum Example. Addition of multiple independent Exponential random variables <math>\mathbf{X}_{1},\mathbf{X}_{2},\cdots</math> are <math>i.i.d.</math> Exponentail random varia...)
- 11:33, 17 November 2010 (diff | hist) . . (+219) . . ECE 600 Central Limit Theorem
- 11:32, 17 November 2010 (diff | hist) . . (+413) . . ECE 600 Central Limit Theorem
- 11:16, 17 November 2010 (diff | hist) . . (+2,851) . . N ECE 600 Central Limit Theorem (New page: 2.5 Central limit theorem Let <math>\left\{ \mathbf{X}_{n}\right\}</math> be a sequence of <math>i.i.d.</math> random vectors with mean <math>\mu</math> and variance <math>\sigma^{2}<...)
- 11:10, 17 November 2010 (diff | hist) . . (+607) . . N ECE 600 Strong law of large numbers (Borel) (New page: 2.4 Strong law of large numbers (Borel) Let <math>\left\{ \mathbf{X}_{n}\right\}</math> be a sequence of identically distributed random variables with mean <math>\mu</math> and varianc...)
- 11:08, 17 November 2010 (diff | hist) . . (+1,548) . . N ECE 600 Weak law of large numbers (New page: 2.3 Weak law of large numbers Let <math>\left\{ \mathbf{X}_{n}\right\}</math> be a sequence of <math>i.i.d.</math> random variables with mean <math>\mu</math> and variance <math>\sigm...)
- 11:04, 17 November 2010 (diff | hist) . . (+2,368) . . N ECE 600 Chebyshev Inequality (New page: 2.2 Chebyshev inequality Let <math>\mathbf{X}</math> be a random variable with mean <math>\mu</math> and variance <math>\sigma^{2}</math> . Then <math>\forall\epsilon>0</math> <math>p...)
- 10:58, 17 November 2010 (diff | hist) . . (+235) . . ECE 600 Convergence
- 07:25, 17 November 2010 (diff | hist) . . (+599) . . ECE 600 Convergence
- 06:55, 17 November 2010 (diff | hist) . . (+256) . . ECE 600 Convergence
- 06:41, 17 November 2010 (diff | hist) . . (+8,147) . . N ECE 600 Convergence (New page: ='''2.1 Converge'''= Definition. Converge A sequence of numbers <math>x_{1},x_{2},\cdots,x_{n},\cdots</math> is said to converge to a limit <math>x</math> if, for every <math>\epsilon>...)
- 06:23, 17 November 2010 (diff | hist) . . (+993) . . N ECE 600 Sequences of Random Variables (New page: Definition A random sequence or a discrete-time random process is a sequence of random variables <math>\mathbf{X}_{1},\cdots,\mathbf{X}_{n},\cdots</math> defined on a probability space <...)
- 06:16, 17 November 2010 (diff | hist) . . (+317) . . 2010 Fall ECE 600 Comer
- 06:10, 17 November 2010 (diff | hist) . . (+32) . . ECE 600 Prerequisites Poisson Random Process
- 06:09, 17 November 2010 (diff | hist) . . (+89) . . ECE 600 Prerequisites etc.
- 06:08, 17 November 2010 (diff | hist) . . (+271) . . N ECE 600 Prerequisites etc. (New page: ='''1.13 etc.'''= Inner product space Any Euclidean space <math>\mathbf{R}^{n}</math> with dot product is an inner product space. <math>\left\langle \left(x_{1},\cdots,x_{n}\right),\le...)
- 06:07, 17 November 2010 (diff | hist) . . (+1,312) . . N ECE 600 Prerequisites Minimum Mean-Square Error Estimation (New page: ='''1.12 Minimum Mean-Square Error Estimation'''= Let <math>\mathbf{X}</math> and <math>\mathbf{Y}</math> be two jointly-distributed RVs, suppose we want to estimate the value of <math>...)
- 06:03, 17 November 2010 (diff | hist) . . (+24) . . ECE 600 Prerequisites Joint Characteristic Function
- 06:01, 17 November 2010 (diff | hist) . . (+3,952) . . N ECE 600 Prerequisites Joint Characteristic Function (New page: ='''1.11 Joint Characteristic Function'''= The joint characteristic function of two joint-distributed RVs <math>\mathbf{X}</math> and <math>\mathbf{Y}</math> is <math>\Phi_{\mathbf{XY...)
- 05:54, 17 November 2010 (diff | hist) . . (+4,876) . . N ECE 600 Prerequisites Two Random Variables (New page: ='''1.10 Two Random Variables'''= '''Fact''' Let <math>\mathbf{X}</math> and <math>\mathbf{Y}</math> be two jointly-distributed, statistically independent random variables, having pdfs...)
- 05:41, 17 November 2010 (diff | hist) . . (+962) . . N ECE 600 Prerequisites Direct PDF Method (New page: ='''1.9 Direct PDF Method'''= If <math>y=g\left(x\right)\Longrightarrow x=g^{-1}\left(y\right)</math> uniquely, then <math>f_{\mathbf{Y}}\left(y\right)=f_{\mathbf{X}}\left(g^{-1}\left(y...)
- 05:39, 17 November 2010 (diff | hist) . . (+1,608) . . N ECE 600 Prerequisites Some Measures of Random Variables (New page: ='''1.8 Some Measures on Random Variable'''= 1.8.1 Mean <math>E\left[\mathbf{X}\right]=\sum_{k}k\cdot p_{\mathbf{X}}\left(k\right)=\int_{-\infty}^{\infty}x\cdot f_{\mathbf{X}}\left(x\rig...)
- 05:30, 17 November 2010 (diff | hist) . . (+435) . . N ECE 600 Prerequisites CDF (Cumulative Distribution Function) and PDF (Probability Density Function) (New page: ='''1.7 CDF (Cumulative Distribution Function) and PDF (Probability Density Function)'''= <math>F_{\mathbf{X}}\left(x\right)=P\left(\left\{ \mathbf{X}\leq x\right\} \right)</math> <math...)
- 05:28, 17 November 2010 (diff | hist) . . (+13) . . ECE 600 Prerequisites Continuous Random Variables
- 05:27, 17 November 2010 (diff | hist) . . (+4,446) . . N ECE 600 Prerequisites Continuous Random Variables (New page: ='''1.6 Continuous Random Variables'''= '''1.6.1 Gaussian distribution (normal distribution)''' <math>\mathcal{N}\left(\mu,\sigma^{2}\right)</math> <math>f_{\mathbf{X}}(x)=\frac{1}{\sqr...)
- 12:49, 16 November 2010 (diff | hist) . . (+7) . . ECE 600 Prerequisites Poisson Random Process
- 12:48, 16 November 2010 (diff | hist) . . (+7) . . ECE 600 Prerequisites Discrete Random Variables
- 12:48, 16 November 2010 (diff | hist) . . (+7) . . ECE 600 Prerequisites Bayes' Theorem
- 12:48, 16 November 2010 (diff | hist) . . (+7) . . ECE 600 Prerequisites Probability Space
- 12:47, 16 November 2010 (diff | hist) . . (+7) . . ECE 600 Prerequisites Basic Math
- 12:42, 16 November 2010 (diff | hist) . . (+4,531) . . ECE 600 Prerequisites Poisson Random Process
- 12:27, 16 November 2010 (diff | hist) . . (+48) . . N ECE 600 Prerequisites Poisson Random Process (New page: *ECE 600 Prerequisites)
- 12:26, 16 November 2010 (diff | hist) . . (+2,576) . . ECE 600 Prerequisites Discrete Random Variables
- 12:18, 16 November 2010 (diff | hist) . . (+2,115) . . N ECE 600 Prerequisites Discrete Random Variables (New page: =='''1.4 Discrete Random Variables'''== ='''1.4.1 Bernoulli distribution'''= <math>\mathbf{X}=\begin{cases} \begin{array}{lll} 1 & & ,\text{ if success}\\ 0 & & ,\text{ if fail.} \end{...)
- 12:10, 16 November 2010 (diff | hist) . . (+2) . . ECE 600 Prerequisites
- 12:09, 16 November 2010 (diff | hist) . . (+462) . . ECE 600 Prerequisites Bayes' Theorem
- 12:07, 16 November 2010 (diff | hist) . . (+48) . . N ECE 600 Prerequisites Bayes' Theorem (New page: *ECE 600 Prerequisites)
- 12:04, 16 November 2010 (diff | hist) . . (+268) . . ECE 600 Prerequisites Probability Space
- 11:56, 16 November 2010 (diff | hist) . . (+2,844) . . N ECE 600 Prerequisites Probability Space (New page: =='''1.2 Probability Space'''== ='''1.2.1 Probability Space'''= • Probability Space = <math>\left\{ \mathcal{S},\mathcal{F}\left(\mathcal{S}\right),\mathcal{P}\right\}</math> • <m...)
- 11:47, 16 November 2010 (diff | hist) . . (+51) . . ECE 600 Prerequisites Basic Math
- 11:45, 16 November 2010 (diff | hist) . . (+2) . . ECE 600 Prerequisites Basic Math
- 11:43, 16 November 2010 (diff | hist) . . (-13) . . ECE 600 Prerequisites Basic Math
- 11:39, 16 November 2010 (diff | hist) . . (+1,341) . . ECE 600 Prerequisites Basic Math
- 11:34, 16 November 2010 (diff | hist) . . (+1,762) . . ECE 600 Prerequisites Basic Math
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