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- Let <math class="inline">\mathbf{X}</math> be a random variable with mean <math class="inline">\mu</math> and variance <math clas [[ECE 600 Sequences of Random Variables|Back to Sequences of Random Variables]]3 KB (435 words) - 11:38, 30 November 2010
- ...ght\}</math> be a sequence of <math class="inline">i.i.d.</math> random variables with mean <math class="inline">\mu</math> and variance <math class="inline [[ECE 600 Sequences of Random Variables|Back to Sequences of Random Variables]]2 KB (303 words) - 11:39, 30 November 2010
- ...bf{X}_{n}\right\}</math> be a sequence of identically distributed random variables with mean <math class="inline">\mu</math> and variance <math class="inline [[ECE 600 Sequences of Random Variables|Back to Sequences of Random Variables]]795 B (126 words) - 11:41, 30 November 2010
- [[Category:random variables]] ...[ECE_600_Sequences_of_Random_Variables|course notes on "sequence of random variables"]] of [[user:han84|Sangchun Han]], [[ECE]] PhD student.4 KB (657 words) - 11:42, 30 November 2010
- =2.6 Random Sum= Example. Addition of multiple independent Exponential random variables2 KB (310 words) - 11:44, 30 November 2010
- [[Category:random variables]]525 B (66 words) - 13:11, 22 November 2010
- ...ead of mapping each <math class="inline">\omega\in\mathcal{S}</math> of a random experiment to a number <math class="inline">\mathbf{X}\left(\omega\right)</ ...andom about the sample functions. The randomness comes from the underlying random experiment.16 KB (2,732 words) - 11:47, 30 November 2010
- ...cdots</math> be a sequence of independent, identically distributed random variables, each having pdf ...ht)}\left(x\right).</math> Let <math class="inline">Y_{n}</math> be a new random variable defined by10 KB (1,713 words) - 07:17, 1 December 2010
- ...class="inline">\mathbf{X}\left(t,\omega\right)</math> , then we have a new random process <math class="inline">\mathbf{Y}\left(t\right)</math> : <math class= We will assume that <math class="inline">T</math> is deterministic (NOT random). Think of <math class="inline">\mathbf{X}\left(t\right)=\text{input to a s11 KB (1,964 words) - 11:52, 30 November 2010
- [[Category:random variables]] We place at random n points in the interval <math class="inline">\left(0,1\right)</math> and5 KB (859 words) - 11:55, 30 November 2010
- ...endent Poisson random variables|Addition of two independent Poisson random variables]] ...dent Gaussian random variables|Addition of two independent Gaussian random variables]]1 KB (188 words) - 11:57, 30 November 2010
- ...1 dime. One of the boxes is selected at random, and a coin is selected at random from that box. The coin selected is a quater. What is the probability that – A = Box selected at random contains at least one dime.22 KB (3,780 words) - 07:18, 1 December 2010
- ...th> be a sequence of random variables that converge in mean square to the random variable <math class="inline">\mathbf{X}</math> . Does the sequence also co ...> A sequence of random variable that converge in mean square sense to the random variable <math class="inline">\mathbf{X}</math> , also converges in probabi6 KB (1,093 words) - 08:23, 27 June 2012
- Consider the following random experiment: A fair coin is repeatedly tossed until the same outcome (H or T ...math> , respectively. Let <math class="inline">\mathbf{Z}</math> be a new random variable defined as <math class="inline">\mathbf{Z}=\mathbf{X}+\mathbf{Y}.<10 KB (1,827 words) - 08:33, 27 June 2012
- ...irst coin is fair and the second coin has two heads. One coin is picked at random and tossed two times. It shows heads both times. What is the probability th ...mathbf{Y}_{t}</math> by jointly wide sense stationary continous parameter random processes with <math class="inline">E\left[\left|\mathbf{X}\left(0\right)-\9 KB (1,534 words) - 08:33, 27 June 2012
- ...ft(x\right)=P\left(\left\{ \mathbf{X}\leq x\right\} \right)</math> of the random variable <math class="inline">\mathbf{X}</math> . Make sure and specify you ...inline">\mathbf{Y}</math> is <math class="inline">r</math> . Define a new random variable <math class="inline">\mathbf{Z}</math> by <math class="inline">\m10 KB (1,652 words) - 08:32, 27 June 2012
- ...inline">\mathbf{Y}</math> be jointly Gaussian (normal) distributed random variables with mean <math class="inline">0</math> , <math class="inline">E\left[\math ...}</math> . Note: <math class="inline">\mathbf{V}</math> is not a Gaussian random variable.6 KB (916 words) - 08:26, 27 June 2012
- State the definition of a random variable; use notation from your answer in part (a). A random variable <math class="inline">\mathbf{X}</math> is a process of assigning10 KB (1,608 words) - 08:31, 27 June 2012
- ...f{Y}</math> be two independent identically distributed exponential random variables having mean <math class="inline">\mu</math> . Let <math class="inline">\mat ...that it deals with the exponential random variable rather than the Poisson random variable.14 KB (2,358 words) - 08:31, 27 June 2012
- Assume that <math class="inline">\mathbf{X}</math> is a binomial distributed random variable with probability mass function (pmf) given by <math class="inline" ...athbf{X}_{n},\cdots</math> be a sequence of binomially distributed random variables, with <math class="inline">\mathbf{X}_{n}</math> having probability mass f10 KB (1,754 words) - 08:30, 27 June 2012
- ...d <math class="inline">\mathbf{Y}</math> be two joinly distributed random variables having joint pdf Let <math class="inline">\mathbf{Z}</math> be a new random variable defined as <math class="inline">\mathbf{Z}=\mathbf{X}+\mathbf{Y}</9 KB (1,560 words) - 08:30, 27 June 2012
- ...ependent, identically distributed zero-mean, unit-variance Gaussian random variables. The sequence <math class="inline">\mathbf{X}_{n}</math> , <math class="inl ...ath class="inline">\mathbf{X}_{n}</math> is a sequence of Gaussian random variables with zero mean and variance <math class="inline">\sigma_{\mathbf{X}_{n}}^{214 KB (2,439 words) - 08:29, 27 June 2012
- ...line">\mathbf{Y}</math> be two independent identically distributed random variables taking on values in <math class="inline">\mathbf{N}</math> (the natural nu ...y distributed random variables, with the <math class="inline">n</math> -th random variable <math class="inline">\mathbf{X}_{n}</math> having pmf <math class10 KB (1,636 words) - 08:29, 27 June 2012
- ...athbf{X}_{2},\mathbf{X}_{3},\cdots</math> is a sequence of i.i.d. random variables with finite mean <math class="inline">E\left[\mathbf{X}_{i}\right]=\mu</mat ...{2},\mathbf{X}_{3},\cdots</math> be a sequence of i.i.d Bernoulli random variables with <math class="inline">p=1/2</math> , and let <math class="inline">\math12 KB (1,920 words) - 08:28, 27 June 2012
- =Example. Addition of two independent Poisson random variables= ...and <math class="inline">\mathbf{Y}</math> are independent Poisson random variables with means <math class="inline">\lambda</math> and <math class="inline">\m3 KB (532 words) - 11:58, 30 November 2010
- =Example. Addition of two independent Gaussian random variables= ...is the pdf you determined in part (b)? What is the mean and variance of a random variable with this pdf?7 KB (1,015 words) - 11:59, 30 November 2010
- =Example. Addition of two jointly distributed Gaussian random variables= ...inline">\mathbf{Y}</math> is <math class="inline">r</math> . Define a new random variable <math class="inline">\mathbf{Z}=\mathbf{X}+\mathbf{Y}</math> .3 KB (504 words) - 12:00, 30 November 2010
- =Example. Two jointly distributed random variables= Two joinly distributed random variables <math class="inline">\mathbf{X}</math> and <math class="inline">\mathbf{Y}2 KB (416 words) - 11:47, 3 December 2010
- =Example. Two jointly distributed independent random variables= ..."inline">\mathbf{Y}</math> be two jointly distributed, independent random variables. The pdf of <math class="inline">\mathbf{X}</math> is5 KB (803 words) - 12:08, 30 November 2010
- =Example. Two jointly distributed independent random variables= ..."inline">\mathbf{Y}</math> be two jointly distributed, independent random variables. The pdf of <math class="inline">\mathbf{X}</math> is5 KB (803 words) - 12:10, 30 November 2010
- =Example. Geometric random variable= Let <math class="inline">\mathbf{X}</math> be a random variable with probability mass function5 KB (793 words) - 12:10, 30 November 2010
- =Example. Sequence of binomially distributed random variables= ...of binomially distributed random variables, with the <math>n_{th}</math> random variable <math>\mathbf{X}_{n}</math> having pmf3 KB (470 words) - 13:02, 23 November 2010
- =Example. Sequence of binomially distributed random variables= ...distributed random variables, with the <math class="inline">n_{th}</math> random variable <math class="inline">\mathbf{X}_{n}</math> having pmf3 KB (539 words) - 12:14, 30 November 2010
- =Example. Sequence of exponentially distributed random variables= ...X}_{n}</math> be a collection of i.i.d. exponentially distributed random variables, each having mean <math class="inline">\mu</math> . Define3 KB (486 words) - 07:13, 1 December 2010
- =Example. Sequence of uniformly distributed random variables= ...erval <math class="inline">\left[0,1\right]</math> . Define the new random variables <math class="inline">\mathbf{W}=\max\left\{ \mathbf{X}_{1},\mathbf{X}_{2},\3 KB (456 words) - 07:14, 1 December 2010
- =Example. Mean of i.i.d. random variables= ...ath> be <math class="inline">M</math> jointly distributed i.i.d. random variables with mean <math class="inline">\mu</math> and variance <math class="inline2 KB (420 words) - 11:25, 16 July 2012
- =Example. A sum of a random number of i.i.d. Gaussians= ...{ \mathbf{X}_{n}\right\}</math> be a sequence of i.i.d. Gaussian random variables, each having characteristic function2 KB (426 words) - 07:15, 1 December 2010
- ...ot certain what it says in revers, but I have to believe that whatever the random collection of notes is that would be produced by playing it in reverse woul %Note funtion takes 2 variables4 KB (570 words) - 12:13, 15 January 2011
- * [[Methods of generating random variables|Methods of generating random variables, a class project by Zhenming Zhang]] * [[Applications of Poisson Random Variables|Applications of Poisson Random Variables, a class project by Trevor Holloway]]1 KB (195 words) - 07:52, 15 May 2013
- *Discrete Random Variables ...on_ECE302S13Boutin|Normalizing the probability mass function of a discrete random variable]]7 KB (960 words) - 18:17, 23 February 2015
- ...noisy data set. Complex data sets may hid significant relationship between variables, and the aim of PCA is to extricate those relevant information shrouded by ...three dimensional world, so we decide to set up three cameras in a rather random directions to collect the data on the motion of the spring.6 KB (1,043 words) - 12:45, 3 March 2015
- ...ce of random variables since <math>p_i(\vec{x_0})</math> depends on random variables |sample_space_i|. What do we mean by convergence of a sequence of random variables (There are many definitions). We pick "Convergence in mean square" sense, i8 KB (1,246 words) - 11:21, 10 June 2013
- The linear combination of independent Gaussian random variables is also Gaussian. ...</math> are <math>n</math> independent Gaussian random variables, then the random variable <math>Y</math> is also Gaussian, where <math>Y</math> is a linear2 KB (453 words) - 14:19, 13 June 2013
- ...h>M_{Xi}(t)</math>, <math>i = 1,2,...,n</math>, and if <math>Y</math> is a random variable resulting from a linear combination of <math>X_i</math>s such that ...s can be written as the product of the expectations of functions of random variables (proof). <br/>1 KB (261 words) - 14:17, 13 June 2013
- ...s value, which is also an address.<br>• Nothing is changed to the actual variables in the main function so the output is still 12 -9<br>• Since none of the ...like stack memory. <br>Stack Memory: first in → last out<br>Heap Memory: random access<br>However, it means that you need to allocate and release. You need3 KB (540 words) - 09:24, 13 February 2012
- | [[Media:Walther_MA375_02February2012.pdf| Bernoulli Trials,Random Variables]]3 KB (418 words) - 06:38, 21 March 2013
- Deterministic (single, non-random) estimate of parameters, theta_ML ...Bayesian formulation, the parameters to be estimated are treated as random variables. The Bayes estimate is the one that minimizes the Bayes risk by minimizing6 KB (976 words) - 13:25, 8 March 2012
- [[Category:random variables]] Question 1: Probability and Random Processes3 KB (406 words) - 10:19, 13 September 2013
- [[Category:random variables]] Question 1: Probability and Random Processes5 KB (763 words) - 10:57, 10 March 2015
- [[Category:random variables]] Question 1: Probability and Random Processes5 KB (780 words) - 01:25, 9 March 2015
