Create the page "Random variables" on this wiki! See also the search results found.
- 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
- [[Category:random variables]] Question 1: Probability and Random Processes5 KB (766 words) - 00:16, 10 March 2015
- [[Category:random variables]] Question 1: Probability and Random Processes5 KB (729 words) - 00:51, 10 March 2015
- [[Category:random variables]] Question 1: Probability and Random Processes5 KB (735 words) - 01:17, 10 March 2015
- [[Category:random variables]] Question 1: Probability and Random Processes4 KB (609 words) - 01:54, 10 March 2015
- [[Category:random variables]] Question 1: Probability and Random Processes5 KB (726 words) - 10:35, 10 March 2015
- [[Category:random variables]] Question 1: Probability and Random Processes4 KB (632 words) - 11:05, 10 March 2015
- [[Category:random variables]] Question 1: Probability and Random Processes4 KB (643 words) - 11:16, 10 March 2015
- [[Category:random variables]] Question 1: Probability and Random Processes4 KB (616 words) - 10:19, 13 September 2013
- [[Category:random variables]] Question 1: Probability and Random Processes4 KB (572 words) - 10:24, 10 March 2015
- [[Category:random variables]] Question 1: Probability and Random Processes5 KB (748 words) - 01:01, 10 March 2015
- [[Category:random variables]] Question 1: Probability and Random Processes2 KB (358 words) - 10:33, 13 September 2013
- [[Category:random variables]] Question 1: Probability and Random Processes4 KB (638 words) - 10:34, 13 September 2013
- [[Category:random variables]] Question 1: Probability and Random Processes2 KB (248 words) - 10:34, 13 September 2013
- [[Category:random variables]] Question 1: Probability and Random Processes2 KB (282 words) - 10:34, 13 September 2013
- [[Category:random variables]] Question 1: Probability and Random Processes3 KB (532 words) - 10:36, 13 September 2013
- [[Category:random variables]] Question 1: Probability and Random Processes4 KB (655 words) - 10:36, 13 September 2013
- [[Category:random variables]] Question 1: Probability and Random Processes2 KB (357 words) - 10:36, 13 September 2013
- [[Category:random variables]] Question 1: Probability and Random Processes2 KB (234 words) - 10:37, 13 September 2013
- [[Category:random variables]] Question 1: Probability and Random Processes3 KB (496 words) - 10:37, 13 September 2013
- [[Category:random variables]] Question 1: Probability and Random Processes4 KB (547 words) - 16:40, 30 March 2015
- ...25 pts} \right) \text{ Let X, Y, and Z be three jointly distributed random variables with joint pdf} f_{XYZ}\left ( x,y,z \right )= \frac{3z^{2}}{7\sqrt[]{2\pi}5 KB (711 words) - 09:05, 27 July 2012
- [[Category:random variables]] Question 1: Probability and Random Processes8 KB (1,247 words) - 10:29, 13 September 2013
- [[Category:random variables]] Question 1: Probability and Random Processes6 KB (932 words) - 10:30, 13 September 2013
- Probability, Statistics, and Random Processes for Electrical Engineering, 3rd Edition, by Alberto Leon-Garcia, *Discrete Random Variables10 KB (1,422 words) - 20:14, 30 April 2013
- ==Part 2: Discrete Random Variables (To be tested in the second intra-semestrial exam)== *2.2 Functions of a discrete random variable4 KB (498 words) - 10:18, 17 April 2013
- ...e having trouble using the image() command in Matlab for displaying their 'random image' in part 2? Mine comes up as just a black square every time. I set th ...ifferent numbers of arguments. I'd like to not have to create 25 different variables for each window. Can anyone help me with this?5 KB (957 words) - 08:11, 9 April 2013
- ...The formula for obtaining the probability mass function of a function of a random variable was given, and we illustrated it with two simple examples. We fini2 KB (307 words) - 10:26, 4 February 2013
- In Lecture 10, defined the concept of a discrete random variables and gave several examples. The concept that caused the most confusion seems2 KB (289 words) - 11:08, 30 January 2013
- ...the random variable does not change the variance, and that multiplying the random variable by a constant "a" has the effect of multiplying the variance by <m2 KB (336 words) - 12:59, 18 February 2013
- ...n Part III of the material with a definition of the concept of "continuous random variable" along with two examples.2 KB (321 words) - 11:12, 15 February 2013
- ...tative robot spiraling 'inward' or 'outward'. Normally distributed random variables are used to modify the magnitude (M) of the complex vector and rotate the v % generate random initial state with complex magnitude 12 KB (289 words) - 15:14, 1 May 2016
- ...t it is spades, and both probabilities sum up to 1 (since we only have two variables). We can therefore use the following decision rule; that if ''P(x<sub>1</su ...r), we can describe this as a variable ''y'' and we consider ''y'' to be a random variable whose distribution depends on the state of the card and is express5 KB (844 words) - 23:32, 28 February 2013
- ...looked at an example of continuous random variable, namely the exponential random variable.2 KB (329 words) - 08:16, 20 February 2013
- In Lecture 19, we continued our discussion of continuous random variables. ...outin|Invent a problem about the expectation and/or variable of a discrete random variable]]2 KB (252 words) - 08:20, 20 February 2013
- ...discrete) and we began discussing normally distributed (continuous) random variables. ...on_ECE302S13Boutin|Normalizing the probability mass function of a Gaussian random variable]]2 KB (304 words) - 07:43, 23 February 2013
- ...a normally distributed random variable: it was observed that the resulting random variable Y=aX+b is also normally distributed. The relation between the mean3 KB (393 words) - 08:21, 27 February 2013
- ...lso had a little bit of time to start talking about two dimensional random variables.3 KB (387 words) - 07:09, 28 February 2013
- [[Category:independent random variables]] ...e Problem]]: obtaining the joint pdf from the marginals of two independent variables =2 KB (394 words) - 12:03, 26 March 2013
- ...on_ECE302S13Boutin|Normalizing the probability mass function of a Gaussian random variable]] ...13Boutin|Obtaining the joint pdf from the marginal pdfs of two independent variables]]2 KB (337 words) - 06:28, 1 March 2013
- ...of a 2D random variable. In particular, we looked at the covariance of two variables. We finished the lecture by giving the definition of conditional probabili2 KB (324 words) - 13:11, 5 March 2013
- ...ind the pdf of a random variable Y defined as a function Y=g(X) of another random variable X.2 KB (328 words) - 04:58, 9 March 2013
- ...particular, we obtain a formula for the pdf of a sum of independent random variables (namely, the convolution of their respective pdf's).2 KB (286 words) - 09:11, 29 March 2013
- [[Category:independent random variables]] Two continuous random variables X and Y have the following joint probability density function:2 KB (290 words) - 10:17, 27 March 2013
- A discrete random variables X has a moment generating (characteristic) function <math>M_X(s)</math> suc1 KB (211 words) - 03:47, 27 March 2013
- ...vation of the conditional distributions for continuous and discrete random variables, you may wish to go over Professor Mary Comer's [[ECE600_F13_rv_conditional * Alberto Leon-Garcia, ''Probability, Statistics, and Random Processes for Electrical Engineering,'' Third Edition4 KB (649 words) - 13:08, 25 November 2013
- [[Category:normal random variable]] be a two-dimensional Gaussian random variable with mean <math>\mu</math> and standard deviation matrix <math>\Si2 KB (273 words) - 03:22, 26 March 2013
- ...tudent, and let Y be the arrival time of the professor. Assume that the 2D random variable (X,Y) is uniformly distributed in the square [2 , 3]x[2,3]. '''2.''' Let (X,Y) be a 2D random variable that is uniformly distributed in the rectangle [1,3]x[5,10].3 KB (559 words) - 07:02, 22 March 2013
- ...also a quiz where we re-emphasized how easy it is to compute the mean of a random variable with a symmetric pmf/pdf. (The trick is to guess the answer m, and *Read Sections 2.1.1-2.1.6 of Prof. Pollak's notes on random variables [https://engineering.purdue.edu/~ipollak/ee438/FALL04/notes/Section2.1.pdf2 KB (330 words) - 06:16, 9 April 2013
- [[Category:random process]] ...ariable with the same distribution as the random variable contained in the random process at the time found by differencing the two distinct times mentioned9 KB (1,507 words) - 16:23, 23 April 2013
- ...short introduction to the topic, we covered the definition of a stationary random process.3 KB (376 words) - 10:23, 17 April 2013
