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- ='''1.5 Poisson Process'''= ...left\{ \mathbf{N}\left(t\right),\; t\geq0\right\}</math> is the Poinsson process. The distribution of <math class="inline">\mathbf{N}\left(t\right)</math>5 KB (920 words) - 11:26, 30 November 2010
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- <strong>Digital Systems</strong> = system that can process a ditital signal.<br/> <li>Deterministic vs. random3 KB (532 words) - 06:43, 16 September 2013
- I cannot write the process of this demonstration due to the limited environment to draw integral. In this case, it is sure that we have to utilize the exponential random variable method.1 KB (248 words) - 21:14, 4 October 2008
- The next morning all n prisoners will be lined up, in random order, If anyone does not follow the rules, he is executed and the process5 KB (756 words) - 08:23, 20 May 2013
- What is it? Sampling is a process of measuring a CT signal x(t) at some specific values of time t. Let <math>x(t)\,</math> be a random signal with frequency <math>\omega \,</math>2 KB (367 words) - 11:27, 7 November 2008
- ...dom variable" being 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
- the underlying process that generated the data. The contributions of this special issue cover a wi ...rocedure consists of starting with k groups which each consist of a single random point, and thereafter adding the points one after another to the group whos39 KB (5,715 words) - 10:52, 25 April 2008
- So, our aim would be to move from a given random point on the surface towards the global minimum. The contour plots are ofte ...at every point, is the one that yields minimum expense of energy, and this process is continued until the directional derivative becomes zero, which means tha2 KB (336 words) - 14:53, 16 March 2008
- ...ovides the foundations for the understanding of digital signals and how to process them (photos, songs,etc). If you do the homework and go to class you are fi ...we spend on reviewing 301 material and spend more time on image and random process. -- [[User:xiao1|Yimin Xiao]]17 KB (3,004 words) - 08:11, 15 December 2011
- ...tral density functions. Random processes and response of linear systems to random inputs.<br/><br/> <br/>ii. an ability to model complex families of signals by means of random processes.2 KB (231 words) - 07:20, 4 May 2010
- ...dom variable" being 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
- [[Category:random variables]] *[[ECE 600 Prerequisites Discrete Random Variables|Discrete Random Variables]]1 KB (139 words) - 13:13, 16 November 2010
- ='''1.5 Poisson Process'''= ...left\{ \mathbf{N}\left(t\right),\; t\geq0\right\}</math> is the Poinsson process. The distribution of <math class="inline">\mathbf{N}\left(t\right)</math>5 KB (920 words) - 11:26, 30 November 2010
- ='''1.6 Continuous Random Variables'''= ...tribution, then <math class="inline">\mathbf{Y}=\ln\mathbf{X}</math> is a random variable with Gaussian distribution. This distribution is characterized wit5 KB (843 words) - 11:27, 30 November 2010
- [[Category:random variables]] =Sequences of Random Variables=1 KB (194 words) - 11:35, 30 November 2010
- Stochastic process ...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)</16 KB (2,732 words) - 11:47, 30 November 2010
- ...}_{n},\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
- ...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="inline" 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
- The power spectrum or power spectral density (PSD) of a W.S.S. random process <math class="inline">\mathbf{X}\left(t\right)</math> , real or complex, is The PSD gives the average distribution of power in frequency for a random process.3 KB (492 words) - 11:53, 30 November 2010
- ...lass="inline">\mathbf{Y}\left(t\right)</math> be the “smoothed” random process given by <math class="inline">\mathbf{Y}\left(t\right)=\frac{1}{2T}\int_{t- ...be two zero-mean statistically independent, jointly wide-sense stationary random processes. Then the cross-correlation function <math class="inline">R_{\mat3 KB (498 words) - 07:16, 1 December 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
- ...<math class="inline">q=1-p</math> . Given that a set of twins selected at random are of the same sex, what is the probability they are fraternal? ...ts <math class="inline">\mathbf{X}</math> in a baseball game is a Poisson random variable. If the probability of a no-hit game is 1/3 , what is the probabil12 KB (2,205 words) - 07:20, 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
- ...class="inline">\mathbf{Y}</math> be jointly Gaussian (normal) distributed random variables with mean <math class="inline">0</math> , <math class="inline">E\ ...}</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 assigning a number <math class="inline">\mathbf{X}\left(\xi\right)</math10 KB (1,608 words) - 08:31, 27 June 2012
- Assume that <math class="inline">\mathcal{S}</math> is the sample space of a random experiment and that <math class="inline">\mathcal{F}_{1}</math> and <math ...<math class="inline">q=1-p</math> . Given that a set of twins selected at random are of the same sex, what is the probability they are fraternal? (Simplify7 KB (1,210 words) - 08:31, 27 June 2012
- ...>\mathbf{Y}</math> be two independent identically distributed exponential random variables having mean <math class="inline">\mu</math> . Let <math class="in ...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" ...dots,\mathbf{X}_{n},\cdots</math> be a sequence of binomially distributed random variables, with <math class="inline">\mathbf{X}_{n}</math> having probabil10 KB (1,754 words) - 08:30, 27 June 2012
- ...th> and <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
- ...of independent, identically distributed zero-mean, unit-variance Gaussian random variables. The sequence <math class="inline">\mathbf{X}_{n}</math> , <math ...les, <math class="inline">\mathbf{X}_{n}</math> is a sequence of Gaussian random variables with zero mean and variance <math class="inline">\sigma_{\mathbf{14 KB (2,439 words) - 08:29, 27 June 2012
- ...ass="inline">\mathbf{Y}</math> be two independent identically distributed random variables taking on values in <math class="inline">\mathbf{N}</math> (the ...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
- ..._{1},\mathbf{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 ...hbf{X}_{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="inl12 KB (1,920 words) - 08:28, 27 June 2012
- Note that the playing process have two key elements, the rhythm and the melody. One should regard the message has no meaning. It's just a random combination of syllables. People make guesses, and when the first impressio2 KB (347 words) - 05:37, 15 January 2011
- ...ulse response and infinite impulse response digital filters; processing of random signals. Speech processing; vocal tract models and characteristics of the s ...icro-integrated systems; properties of materials for MEMS; microelectronic process modules for design and fabrication. Students will prepare a project report17 KB (2,368 words) - 10:53, 6 May 2012
- *Discrete Random Variables ...on_ECE302S13Boutin|Normalizing the probability mass function of a discrete random variable]]7 KB (960 words) - 18:17, 23 February 2015
- ...ne to errors, I hope the lack of sophistication in my language will render process of PCA understandable(without being entirely inaccurate). Principal Component Analysis is a process of extracting useful information from a noisy data set. Complex data sets m6 KB (1,043 words) - 12:45, 3 March 2015
- ...erent but the general theme is there) and how industry handles the project process (similar to class projects just on a much larger scale). I would say the t ...f our career. They really want to see what else you know- can you talk to random people, are you a team player, can you think on your feet, can you be socia20 KB (3,616 words) - 06:10, 2 September 2013
- ...sphere, which is just the basketball that everyone is familiar with. This process of shrinking a loop is illustrated in the picture below. The Poincaré con ...according to the Poincaré conjecture, what you really have (instead of a random blob of play-doh) is just an out-of-shape ball.9 KB (1,549 words) - 06:55, 21 March 2013
- [[Category:random variables]] Question 1: Probability and Random Processes3 KB (406 words) - 10:19, 13 September 2013
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- [[Category:random variables]] Question 1: Probability and Random Processes4 KB (638 words) - 10:34, 13 September 2013
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- [[Category:random variables]] Question 1: Probability and Random Processes4 KB (547 words) - 16:40, 30 March 2015
- [[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
- *Problem 2.62 from the textbook: Probability, Statistics, and Random Processes for Electrical Engineering, 3rd Edition, by Alberto Leon-Garcia, ...values that exist in the envelopes? If not, what is wrong with our thought process?3 KB (542 words) - 10:52, 29 January 2013
- ...the putative robot spiraling 'inward' or 'outward'. Normally distributed random variables are used to modify the magnitude (M) of the complex vector and ro The (first-order, stationary, discrete time, continuous state-space) Markov process representing this simple 'walk' is as follows:2 KB (289 words) - 15:14, 1 May 2016
- ...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 express ...' is greater than ''P(x<sub>1</sub>|y)'' we choose spades. To justify this process, we can also calculate the probability of error when we make a decision. Wh5 KB (844 words) - 23:32, 28 February 2013
- ...[[Category:probability]] [[Category:problem solving]] [[Category:discrete random variable]] [[Category:expectation]] [[Category:variance]] ...ed without defect is r=.9.<br> a)What is the mean and the variance of the process Bob uses? Solve algebraically first, then solve numerically.<br> b)What ef4 KB (757 words) - 06:59, 22 February 2013
- [[Category:continuous random variable]] ...ctice Problem]]: normalizing the probability mass function of a continuous random variable=2 KB (401 words) - 04:52, 4 March 2013
- ...st of the lecture defining what is a discrete-time/continuous-time random process. Then there was a quiz in which we worked on the following [[Temporary_file2 KB (299 words) - 10:26, 22 March 2013
- .... We also introduced the cross-correlation and the cross-covariance of two Random Processes.2 KB (265 words) - 12:15, 25 March 2013
- ...es. In 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
- ...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/Secti2 KB (330 words) - 06:16, 9 April 2013
- ...relationship between the Poisson random process and the binomial counting process.3 KB (395 words) - 06:31, 15 April 2013
- :a) Explain what is the stationary increment property of a random process.1 KB (187 words) - 06:59, 12 April 2013
- [[Category:random process]] ...with the same distribution as the random variable contained in the random process at the time found by differencing the two distinct times mentioned earlier.9 KB (1,507 words) - 16:23, 23 April 2013
- ...inition of a Poisson process, where the process is described as a counting process with 3 properties (time homogeneity, independence, and small interval proba3 KB (363 words) - 10:09, 17 April 2013
- ...irst important fact (Fact 1) was noted, namely that the mean of the output random signal is equal to the mean of the input signal multiplied by the frequency Note that we are now focusing only on continuous-time random processes for lack of time.3 KB (390 words) - 07:17, 24 April 2013
- ...ntroduction to the topic, we covered the definition of a stationary random process.3 KB (376 words) - 10:23, 17 April 2013
- ...covered relates the cross-correlation between the input and and the output random signals to the unit impulse of the system and the autocorrelation of the in ...e function represent (i.e. expected power for frequency f component of the random signal.)4 KB (545 words) - 07:12, 24 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
- Topic: Poisson Process *Let T be the time when first event occurs in a Poisson random process with parameter <math>\lambda</math>. Obtain the pdf of T.675 B (90 words) - 14:49, 25 April 2013
- ...of these different statistical numbers describing relations of datasets or random variables. So, I decided to crack down on some research and bring the impor '''Covariance:''' This is a measure of two random variable’s association with each other.7 KB (1,146 words) - 06:19, 5 May 2013
- ...erive the differential equation and line integral needed for the inversion process using [[ECE637_tomographic_reconstruction_convolution_back_projection_S13_m The number of photons at depth <math>x</math> can be modeled as a Poisson random variable.9 KB (1,390 words) - 07:24, 26 February 2014
- ...se systems. You will frequently need to analyze signals (deterministic and random) in the time and frequency domains. This experiment introduces you to a num your station and determine the PSD of the output noise process. Measure the RMS14 KB (2,228 words) - 12:03, 15 January 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. T15 KB (2,578 words) - 12:13, 21 May 2014
- [[ECE600_F13_notes_mhossain|'''The Comer Lectures on Random Variables and Signals''']] ...ete-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
- What is a Markov chain/process? What can you do with it? And why are people talking about them? <br>[[2014 Outline of the Project:<br>A) What is a Markov Chain? <br>-Stochastic process<br>-Definition of Markov Chain<br>-Concrete examples and several properties19 KB (3,004 words) - 09:39, 23 April 2014
- ...nsforms_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
- *<math> X </math> a measure random variable, random vector, or random process ...implemented by selecting <math>\phi_1\,</math>and <math>\phi_2\,</math> at random with probability p and 1-p, respectively. The level of this test is15 KB (2,306 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
- ...it can be concluded that such methods work well for generation of Gaussian random number for multi-dimensional space. ...readers who do not have background knowledge about probability and random process can easily follow and generate desired outputs. Explanation with screen sha3 KB (490 words) - 16:21, 14 May 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
- ...1,X_2,…,X_N be the Independent and identically distributed (iid) Poisson random variables. Then, we will have a joint frequency function that is the produc ...2,…,X_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. Th13 KB (1,966 words) - 10:50, 22 January 2015
- [[Category:random variables]] Question 1: Probability and Random Processes4 KB (700 words) - 17:48, 13 March 2015
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- State the definition of a random variable; use notation from your answer in part (a). [[Category:random variables]]2 KB (287 words) - 00:52, 10 March 2015
- [[Category:random variables]] Question 1: Probability and Random Processes6 KB (895 words) - 00:41, 10 March 2015
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- ...atistical tools used for studying networks. Social network analysis is the process of investigating social structures through network and graph theories. Sinc ...ways be more cautious once some disease occurs in any random places by any random people. The people one would touch will greater than we think and that lead14 KB (2,465 words) - 20:07, 24 April 2016
- Set the position as a random point inside the search space Pick a random velocity14 KB (2,177 words) - 11:28, 24 April 2016
- [[Category:random variables]] Question 1: Probability and Random Processes3 KB (502 words) - 15:33, 19 February 2019
- The Cantor Comb is a visual depiction of a Cantor set. The process involves generating a set of intervals as defined recursively below: ...d step to forming a fractal from this symmetry is similar to the bisection process of the Cantor Set: we must remove the B section, and recurse on the A secti15 KB (2,450 words) - 00:15, 3 December 2018
- Question 1: Random Variable Since <math>X(t)</math> is a wide sense Gaussian Process <math>\Rightarrow X(t)</math> is SSS.<br>1 KB (263 words) - 16:36, 19 February 2019
- ...es with rate <math>\lambda</math>. Assume that <math>K</math> is a Poisson random variable independent of <math>N_{i}(t)</math> (for all i) and has mean a. L i.(5 points) Statement: <math>\{ N(t), t \geq 0 \}</math> is a Poisson process with rate <math>a \lambda</math>. <br/>5 KB (910 words) - 03:02, 24 February 2019
- ...ing concepts at random. It is my understanding that the way to change this process from jumping from part to part of the calculations to instead take the next3 KB (583 words) - 21:07, 24 April 2019
- ...ing concepts at random. It is my understanding that the way to change this process from jumping from part to part of the calculations to instead take the next4 KB (644 words) - 11:22, 30 April 2019
- ...examples at the bottom of the article show what happens to the output when random white noise, a period of a sawtooth wave, and a period of a square wave are The output signal from the above process will be a varied and random disturbance that gradually smooths out, which is a reasonably simple model3 KB (546 words) - 23:43, 1 December 2019
- ...hange the message into the cipher text. In more advanced cryptography, the process is similar in using a key in calculations with the message to create the ci Now we are ready for the encryption process.18 KB (3,085 words) - 15:13, 7 December 2022
- #Select at random two large prime numbers ''p'' and ''q'' such that <math>p ≠ q</math>. ...ace. This already suggests that it might be worthwhile to look for ways to process information with a quantum rather than a classical computer since a bit onl31 KB (5,039 words) - 17:31, 6 December 2022
- From exactly the same process, we have the best response function for IU Horology Inc., .... While species do not necessarily choose which strategies they adopt, the process of evolution results in those species adopting varied strategies through mu26 KB (4,138 words) - 08:25, 6 December 2022
- <b><font size="+4">Random Number In Modern Computer</font></b> ...ness. But mathematics and numbers are typically thought of as anything but random, and follow strict rules around changing them. For this reason, creating ra14 KB (2,296 words) - 21:49, 5 December 2022
- ...pletely new images. Without getting too technical, GANs work in a two-step process. First, the “generative” step, where the algorithm attempts to create s **Text goes through a “diffusion process”, which essentially adds noise to the text, making it so the art generato15 KB (2,564 words) - 11:25, 29 November 2022
