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- [[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
- '''Methods of Generating Random Variables''' == 1. Generating uniformly distributed random numbers between 0 and 1: U(0,1) ==3 KB (409 words) - 10:05, 17 April 2013
- '''Applications of Poisson Random Variables''' == Poisson Random Variables==5 KB (708 words) - 07:22, 22 April 2013
- ...e different statistical numbers describing relations of datasets or random variables. So, I decided to crack down on some research and bring the important ideas '''Covariance:''' This is a measure of two random variable’s association with each other.7 KB (1,146 words) - 06:19, 5 May 2013
- where <math>X_1</math> and <math>X_2</math> are iid scalar random variables. ...two Gaussian variables, then <math>X</math> is also a Gaussian distributed random variable [[Linear_combinations_of_independent_gaussian_RVs|(proof)]] charac6 KB (1,084 words) - 13:20, 13 June 2013
- ...nations_of_independent_gaussian_RVs|Linear Combinations of Gaussian Random Variables]] ..._RVs_mhossain|Moment Generating Functions of Linear Combinations of Random Variables]]2 KB (227 words) - 11:15, 6 October 2013
- ...is the expectation function, <math>X</math> and <math>Y</math> are random variables with distribution functions <math>f_X(x)</math> and <math>f_Y(y)</math> res where <math>X_i</math>'s are random variables and <math>a_i</math>'s are real constants ∀<math>i=1,2,...,N</math>.3 KB (585 words) - 14:15, 13 June 2013
- Let <math>X</math> and <math>Y</math> be two random variables with variances <math>Var(X)</math> and <math>Var(Y)</math> respectively and By definition, we have that the variance of random variable <math>Z</math> is given by <br/>2 KB (333 words) - 14:17, 13 June 2013
- [[ECE600_F13_notes_mhossain|'''The Comer Lectures on Random Variables and Signals''']] ...ECE 600. Class Lecture. [https://engineering.purdue.edu/~comerm/600 Random Variables and Signals]. Faculty of Electrical Engineering, Purdue University. Fall 2010 KB (1,697 words) - 12:10, 21 May 2014
- '''The Comer Lectures on Random Variables and Signals''' *[[ECE600_F13_rv_definition_mhossain|Random Variables: Definition]]2 KB (227 words) - 12:10, 21 May 2014
- [[ECE600_F13_notes_mhossain|'''The Comer Lectures on Random Variables and Signals''']] ...finition''' <math>\qquad</math> An '''outcome''' is a possible result of a random experiment.20 KB (3,448 words) - 12:11, 21 May 2014
- [[ECE600_F13_notes_mhossain|'''The Comer Lectures on Random Variables and Signals''']] ...es' Theorem. We will see other equivalent expressions when we cover random variables.6 KB (1,023 words) - 12:11, 21 May 2014
- [[ECE600_F13_rv_distribution_mhossain|Next Topic: Random Variables: Distributions]] [[ECE600_F13_notes_mhossain|'''The Comer Lectures on Random Variables and Signals''']]7 KB (1,194 words) - 12:11, 21 May 2014
- [[ECE600_F13_rv_definition_mhossain|Next Topic: Random Variables: Definition]] [[ECE600_F13_notes_mhossain|'''The Comer Lectures on Random Variables and Signals''']]9 KB (1,543 words) - 12:11, 21 May 2014
- [[ECE600_F13_rv_definition_mhossain|Previous Topic: Random Variables: Definitions]]<br/> [[ECE600_F13_notes_mhossain|'''The Comer Lectures on Random Variables and Signals''']]15 KB (2,637 words) - 12:11, 21 May 2014
- [[ECE600_F13_rv_distribution_mhossain|Previous Topic: Random Variables: Distributions]]<br/> ...00_F13_rv_Functions_of_random_variable_mhossain|Next Topic: Functions of a Random Variable]]6 KB (1,109 words) - 12:11, 21 May 2014
- [[ECE600_F13_notes_mhossain|'''The Comer Lectures on Random Variables and Signals''']] <font size= 3> Topic 8: Functions of Random Variables</font size>9 KB (1,723 words) - 12:11, 21 May 2014
- ...13_rv_Functions_of_random_variable_mhossain|Previous Topic: Functions of a Random Variable]]<br/> [[ECE600_F13_notes_mhossain|'''The Comer Lectures on Random Variables and Signals''']]8 KB (1,474 words) - 12:12, 21 May 2014
- [[ECE600_F13_notes_mhossain|'''The Comer Lectures on Random Variables and Signals''']] The pdf f<math>_X</math> of a random variable X is a function of a real valued variable x. It is sometimes usefu5 KB (804 words) - 12:12, 21 May 2014
- [[ECE600_F13_notes_mhossain|'''The Comer Lectures on Random Variables and Signals''']] <font size= 3> Topic 11: Two Random Variables: Joint Distribution</font size>8 KB (1,524 words) - 12:12, 21 May 2014
- [[ECE600_F13_notes_mhossain|'''The Comer Lectures on Random Variables and Signals''']] <font size= 3> Topic 12: Independent Random Variables</font size>2 KB (449 words) - 12:12, 21 May 2014
- [[ECE600_F13_notes_mhossain|'''The Comer Lectures on Random Variables and Signals''']] <font size= 3> Topic 13: Functions of Two Random Variables</font size>9 KB (1,568 words) - 12:12, 21 May 2014
- [[ECE600_F13_notes_mhossain|'''The Comer Lectures on Random Variables and Signals''']] Given random variables X and Y, let Z = g(X,Y) for some g:'''R'''<math>_2</math>→R. Then E[Z] ca7 KB (1,307 words) - 12:12, 21 May 2014
- [[ECE600_F13_notes_mhossain|'''The Comer Lectures on Random Variables and Signals''']] <font size= 3> Topic 15: Conditional Distributions for Two Random Variables</font size>6 KB (1,139 words) - 12:12, 21 May 2014
- [[ECE600_F13_notes_mhossain|'''The Comer Lectures on Random Variables and Signals''']] <font size= 3> Topic 16: Conditional Expectation for Two Random Variables</font size>4 KB (875 words) - 12:13, 21 May 2014
- [[ECE600_F13_notes_mhossain|'''The Comer Lectures on Random Variables and Signals''']] <font size= 3> Topic 17: Random Vectors</font size>12 KB (1,897 words) - 12:13, 21 May 2014
- [[ECE600_F13_notes_mhossain|'''The Comer Lectures on Random Variables and Signals''']] We will now consider infinite sequences of random variables. We will discuss what it means for such a sequence to converge. This will l15 KB (2,578 words) - 12:13, 21 May 2014
- [[ECE600_F13_notes_mhossain|'''The Comer Lectures on Random Variables and Signals''']] ...n discrete-time random processes, but we will now formalize the concept of random process, including both discrete-time and continuous time.10 KB (1,690 words) - 12:13, 21 May 2014
- [[ECE600_F13_notes_mhossain|'''The Comer Lectures on Random Variables and Signals''']] <font size= 3> Topic 20: Linear Systems with Random Inputs</font size>8 KB (1,476 words) - 12:13, 21 May 2014
- [[Category:random variables]] Question 1: Probability and Random Processes3 KB (449 words) - 21:36, 5 August 2018
- <font size="4">Question 1: Probability and Random Processes </font> ...cting your proof, keep in mind that may be either a discrete or continuous random variable.6 KB (995 words) - 09:21, 15 August 2014
- <font size="4">Question 1: Probability and Random Processes </font> ...} \dots </math> be a sequence of independent, identical distributed random variables, each uniformly distributed on the interval [0, 1], an hence having pdf <br12 KB (1,948 words) - 10:16, 15 August 2014
- ...A stochastic process { X(t), t∈T } is an ordered collection of random variables, T where T is the index set and if t is a time in the set, X(t) is the proc ...s that use X1,…,Xn as independently identically distributed (iid) random variables. However, note that states do not necessarily have to be independently iden19 KB (3,004 words) - 09:39, 23 April 2014
- ...between the prior probability and the posterior probability of two random variables or events. Give two events <math>A</math> and <math>B</math>, we may want t19 KB (3,255 words) - 10:47, 22 January 2015
- ...ollows a multivariate Gaussian distribution in 2D. The data comes from two random seed which are of equal probability and are well separated for better illus #Hotelling, H. (1933). Analysis of a complex of statistical variables into principal components. Journal of educational psychology, 24(6), 417.22 KB (3,459 words) - 10:40, 22 January 2015
- ..._S14_MH|Whitening and Coloring Transforms for Multivariate Gaussian Random Variables]] ...'R''' where '''X''' ∈ '''R'''<math>^d</math> is a d-dimensional Gaussian random vector with mean '''μ''' and covariance matrix '''Σ'''. This slecture ass17 KB (2,603 words) - 10:38, 22 January 2015
- The generic situation is that we observe a n-dimensional random vector X with probability<br>density (or mass) function <span class="texhtm <br> Treating <span class="texhtml">''X''<sub>''j''</sub></span> as random variables in the above equations, we have25 KB (4,187 words) - 10:49, 22 January 2015
- ...nd way was using a uniform random variable in vector operations. A uniform random vector of the same size of the whole dataset is first generated, whose each ...asy to understand even for people who do not have deep knowledge in random variables & probabilities. The demonstrations (figures & codes) in MATLAB were good i3 KB (508 words) - 16:12, 14 May 2014
- ...or a given value of θ is denoted by p(x|θ ). It should be noted that the random variable X and the parameter θ can be vector-valued. Now we obtain a set o ...s parameter estimation, the parameter θ is viewed as a random variable or random vector following the distribution p(θ ). Then the probability density func15 KB (2,273 words) - 10:51, 22 January 2015
- ...random variables and probability mass function in case of discrete random variables and 'θ' is the parameter being estimated. ...es) or the probability of the probability mass (in case of discrete random variables)'''12 KB (1,986 words) - 10:49, 22 January 2015
- ...tor, <math> \theta \in \Omega</math>. So for example, after we observe the random vector <math>Y \in \mathbb{R}^{n}</math>, then our objective is to use <mat ...andom vector <math>Y</math>, the estimate, <math>\hat{\theta}</math>, is a random vector. The mean of the estimator, <math>\bar{\theta}</math>, can be comput14 KB (2,356 words) - 20:48, 30 April 2014
- ...by flipping coins (heads or tails). As the size of the sample increases, a random classifier's ROC point migrates towards (0.5,0.5). ...ring the area under the curve, we can tell the accuracy of a classifier. A random guess is just the line y = x with an area of 0.5. A perfect model will have11 KB (1,823 words) - 10:48, 22 January 2015
- \section{Title: Generation of normally distributed random numbers under a binary prior probability} ...a_1)]$, label the sample as class 1, then, continue to generating a normal random number based on the class 1 statistics $(\mu, \sigma)$.16 KB (2,400 words) - 23:34, 29 April 2014
- For discrete random variables, Bayes rule formula is given by, For continuous random variables, Bayes rule formula is given by,7 KB (1,106 words) - 10:42, 22 January 2015
- <font size="4">Generation of normally distributed random numbers from two categories with different priors </font> ...2), 1]</math> and should be labeled as class 2, then, move onto the normal random number generation step with the class 2 statistics like the same way as we18 KB (2,852 words) - 10:40, 22 January 2015
- ...tor, <math> \theta \in \Omega</math>. So for example, after we observe the random vector <math>Y \in \mathbb{R}^{n}</math>, then our objective is to use <mat ...andom vector <math>Y</math>, the estimate, <math>\hat{\theta}</math>, is a random vector. The mean of the estimator, <math>\bar{\theta}</math>, can be comput19 KB (3,418 words) - 10:50, 22 January 2015
- If the data-points from each class are random variables, then it can be proven that the optimal decision rule to classify a point < Therefore, it is desirable to assume that the data-points are random variables, and attempt to estimate <math> P(w_i|x_0) </math>, in order to use it to c9 KB (1,604 words) - 10:54, 22 January 2015
- The principle of how to generate a Gaussian random variable ...od for pseudo random number sampling first. Then, we will explain Gaussian random sample generation method based on Box Muller transform. Finally, we will in8 KB (1,189 words) - 10:39, 22 January 2015
- ...,X_N be the Independent and identically distributed (iid) Poisson random variables. Then, we will have a joint frequency function that is the product of margi ..._N be the Independent and identically distributed (iid) exponential random variables. As P(X=x)=0 when x<0, no samples can sit in x<0 region. Thus, for al13 KB (1,966 words) - 10:50, 22 January 2015
- The K-means algorithm also introduces a set of binary variables to represent assignment of data points to specific clusters: <br /> This set of binary variables is interpreted as follows: if data point <math>n</math> is assigned to clus8 KB (1,350 words) - 10:57, 22 January 2015
- [[Category:random variables]] Question 1: Probability and Random Processes3 KB (470 words) - 07:47, 4 November 2014
