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- =Addition of two independent Poisson random variables = ...athbf{X}</math> and <math>\mathbf{Y}</math> are independent Poisson random variables with means <math>\lambda</math> and <math>\mu</math>, respectively.3 KB (557 words) - 12:11, 25 September 2013
- == 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?6 KB (939 words) - 04:20, 15 November 2010
- == Example. Addition of multiple independent Exponential random variables == ...h parameter <math>\lambda</math> and <math>\mathbf{N}</math> is Geometric random variable with parameter <math>p</math>. Find the distribution of <math>\mat2 KB (268 words) - 04:18, 15 November 2010
- =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. 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
- [[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
Page text matches
- A & B are independent if <math>P(A\cap B)=P(A)P(B)</math> side note: if A&B are independent then P(A|B)=P(A)3 KB (525 words) - 13:04, 22 November 2011
- == Problem 1: Arbitrary Random Variables == Let <math>U</math> be a uniform random variable on [0,1].4 KB (596 words) - 12:57, 22 November 2011
- *The sum of many, small independent things For 2 independent Gaussians:4 KB (722 words) - 13:05, 22 November 2011
- The PDF of the sum of two independent random variables is the convolution of the two PDFs. The lecture notes from 10/10 are helpf133 B (23 words) - 19:13, 19 October 2008
- == Problem 1: Random Point, Revisited== In the following problems, the random point (X , Y) is uniformly distributed on the shaded region shown.4 KB (703 words) - 12:58, 22 November 2011
- ...observed should be the sum or mean of many independent random variables. (variables need not be iid)(See the PROOF ) undirected graphs (Markov random fields), probabilistic decision trees/models have a number of31 KB (4,832 words) - 18:13, 22 October 2010
- ...ormally distributed random numbers : ex) RANDN(N) is an N-by-N matrix with random entries, chosen from a normal distribution with mean zero, variance one and ...ro generate a vecort of n-gaussian random variables ? can this be called a random vector ? BAsically my question is how do we simulate gaussian data whcih h10 KB (1,594 words) - 11:41, 24 March 2008
- which datasets with tens or hundreds of thousands of variables are available. These areas include ...tion of the nearest of a set of previously classified points. This rule is independent of the underlying joint distribution on the sample points and their classif39 KB (5,715 words) - 10:52, 25 April 2008
- ...ion case, there will be very large set of feature vectors and classes, and independent of the probability distributions of features, the sum of the distributions The following histograms of N uniformly distributed random variables for different values of N can be given to visualize the [http://en.wikipedi2 KB (247 words) - 08:32, 10 April 2008
- ...iable" being observed should be the sum or mean of many independent random variables.213 B (35 words) - 10:01, 31 March 2008
- | align="right" style="padding-right: 1em;" | The intersection of two independent events A and B ...e-policy: -moz-initial;" colspan="2" | Expectation and Variance of Random Variables3 KB (491 words) - 12:54, 3 March 2015
- let X1,X2,...,Xn be n independent and identically distributed variables (i.i.d) with finite mean <math>\mu</math> and finite variance <math>\sigma^ More precisely the random variable <math>Z_n = \frac{\Sigma_{i=1}^n X_i - n \mu}{\sigma \sqrt{n}}</ma5 KB (806 words) - 09:08, 11 May 2010
- ...I reduced it to [1 2 3; 0 -3 -3]. I'm not even sure whether plugging in random values was the right idea, but I'm stuck here. How do I proceed from here? ...That's like doing an experiment in science. You'd have to plug in lots of random values if you were doing science, but you'd miss the key points in math. Y4 KB (756 words) - 04:25, 8 September 2010
- ...observed should be the sum or mean of many independent random variables. (variables need not be iid)(See the PROOF ) undirected graphs (Markov random fields), probabilistic decision trees/models have a number of31 KB (4,787 words) - 18:21, 22 October 2010
- = [[ECE]] 600: Random Variables and Stochastic Processes = :*[[ECE 600 Sequences of Random Variables|2. Sequences of Random Variables]]2 KB (238 words) - 12:14, 25 September 2013
- [[Category:random variables]] Question 1: Probability and Random Processes1 KB (191 words) - 17:42, 13 March 2015
- [[Category:random variables]] Question 1: Probability and Random Processes5 KB (928 words) - 17:46, 13 March 2015
- =Addition of two independent Poisson random variables = ...athbf{X}</math> and <math>\mathbf{Y}</math> are independent Poisson random variables with means <math>\lambda</math> and <math>\mu</math>, respectively.3 KB (557 words) - 12:11, 25 September 2013
- == Example. Two jointly distributed random variables == Two joinly distributed random variables <math>\mathbf{X}</math> and <math>\mathbf{Y}</math> have joint pdf7 KB (1,103 words) - 05:27, 15 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?6 KB (939 words) - 04:20, 15 November 2010
- == Example. Addition of multiple independent Exponential random variables == ...h parameter <math>\lambda</math> and <math>\mathbf{N}</math> is Geometric random variable with parameter <math>p</math>. Find the distribution of <math>\mat2 KB (268 words) - 04:18, 15 November 2010
- Two independent Poisson process <math class="inline">\mathbf{N}_{1}\left(t\right)</math> a ...th class="inline">PP\left(\lambda_{i}\right),\; i=1,2,\cdots,n</math> and independent each other. If <math class="inline">\mathbf{N}\left(t\right)=\sum_{i=1}^{n}5 KB (920 words) - 11:26, 30 November 2010
- ='''1.10 Two Random Variables'''= ...bf{Y}</math> be two jointly-distributed, statistically independent random variables, having pdfs <math class="inline">f_{\mathbf{X}}\left(x\right)</math> and6 KB (952 words) - 11:31, 30 November 2010
- =2.6 Random Sum= Example. Addition of multiple independent Exponential random variables2 KB (310 words) - 11:44, 30 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
- ...Are <math class="inline">A</math> and <math class="inline">B^{C}</math> independent? (You must prove your result). <math class="inline">\therefore A\text{ and }B^{C}\text{ are independent. }</math>6 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
- ...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 ...stributed r.v's with identical means and variances but are not necessarily independent. Show that the r.v. <math class="inline">\mathbf{V}=\mathbf{X}+\mathbf{Y}</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 ...athbf{X}</math> and <math class="inline">\mathbf{Y}</math> statistically independent? Justify your answer.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
- =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. 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. 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
- *Discrete Random Variables ...on_ECE302S13Boutin|Normalizing the probability mass function of a discrete random variable]]7 KB (960 words) - 18:17, 23 February 2015
- 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
- [[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 (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 Processes4 KB (655 words) - 10:36, 13 September 2013
- [[Category:random variables]] Question 1: Probability and Random Processes4 KB (547 words) - 16:40, 30 March 2015
- 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
- ...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
- ...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
- [[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
- ...ind the pdf of a random variable Y defined as a function Y=g(X) of another random variable X. **[[Practice_Question_independence_ECE302S13Boutin|Determine if X and Y independent from their joint density]]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]] = [[:Category:Problem solving|Practice Problem]]: Determine if X and Y are independent =2 KB (290 words) - 10:17, 27 March 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
- [[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
- '''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
- ...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
- ...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
- '''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_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_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 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
- [[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> ...} \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 t where <math>C_i</math> is a constant value which is independent of <math>x</math>. Finally, we can use the following discriminant function19 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 ...subcomponents are non-Gaussian signals and that they are all statistically independent from each other.22 KB (3,459 words) - 10:40, 22 January 2015
- ..._S14_MH|Whitening and Coloring Transforms for Multivariate Gaussian Random Variables]] ...y data processing techniques such as [[PCA|principal component analysis]], independent component analysis, etc. This slecture discusses how to whiten data that is17 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 ...ume that samples'''''<math>x_{1}, x_{2} \ldots, x_{N}</math> '''''are independent events. <br>25 KB (4,187 words) - 10:49, 22 January 2015
- ...riable X and the parameter θ can be vector-valued. Now we obtain a set of independent observations or samples S = {x<sub>1</sub>,x<sub>2</sub>,...,x<sub>n</sub>} ...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
- \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
- <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
- 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
- Suppose we have a set of n independent and identically destributed observation samples. Then density function is f As each sample x_i is independent with each other, the likelihood of θ with the data set of samples x_1,x_2,13 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
- [[Category:random variables]] Question 1: Probability and Random Processes3 KB (566 words) - 17:28, 23 February 2017
- [[Category:random variables]] Question 1: Probability and Random Processes5 KB (927 words) - 16:43, 24 February 2017
- [[Category:random variables]] Question 1: Probability and Random Processes3 KB (548 words) - 07:33, 20 November 2014
- [[Category:random variables]] Question 1: Probability and Random Processes2 KB (384 words) - 00:22, 10 March 2015
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- [[Category:random variables]] Question 1: Probability and Random Processes4 KB (646 words) - 10:26, 10 March 2015
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- [[Category:random variables]] Question 1: Probability and Random Processes5 KB (882 words) - 01:54, 31 March 2015
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- [[Category:random variables]] Question 1: Probability and Random Processes2 KB (351 words) - 00:17, 4 December 2015
- [[Category:random variables]] Question 1: Probability and Random Processes4 KB (851 words) - 23:04, 31 January 2016
- For this problem, it is very useful to note that for any independent random variables <math>X</math> and <math>Y</math> and their characteristic functions <math> We then note that the characteristic function of an exponential random variable <math>Z</math> is written as2 KB (243 words) - 22:00, 7 March 2016
- [[Category:random variables]] Question 1: Probability and Random Processes3 KB (502 words) - 15:33, 19 February 2019
