• [[Category:random variables]] Question 1: Probability and Random Processes
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  • [[Category:random variables]] Question 1: Probability and Random Processes
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  • [[Category:random variables]] Question 1: Probability and Random Processes
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  • [[Category:random variables]] Question 1: Probability and Random Processes
    4 KB (638 words) - 10:34, 13 September 2013
  • [[Category:random variables]] Question 1: Probability and Random Processes
    2 KB (248 words) - 10:34, 13 September 2013
  • [[Category:random variables]] Question 1: Probability and Random Processes
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  • [[Category:random variables]] Question 1: Probability and Random Processes
    3 KB (496 words) - 10:37, 13 September 2013
  • [[Category:random variables]] Question 1: Probability and Random Processes
    4 KB (547 words) - 16:40, 30 March 2015
  • [[Category:random variables]] Question 1: Probability and Random Processes
    6 KB (932 words) - 10:30, 13 September 2013
  • Probability, Statistics, and Random Processes for Electrical Engineering, 3rd Edition, by Alberto Leon-Garcia, *Discrete Random Variables
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  • ==Part 2: Discrete Random Variables (To be tested in the second intra-semestrial exam)== *2.2 Functions of a discrete random variable
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  • *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?
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  • ...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. Wh
    5 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 ef
    4 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_file
    2 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/Secti
    2 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 proba
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  • ...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.)
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  • '''Methods of Generating Random Variables''' == 1. Generating uniformly distributed random numbers between 0 and 1: U(0,1) ==
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  • '''Applications of Poisson Random Variables''' == Poisson Random Variables==
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  • 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.
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  • ...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 RMS
    14 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. T
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  • [[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.
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  • [[ECE600_F13_notes_mhossain|'''The Comer Lectures on Random Variables and Signals''']] <font size= 3> Topic 20: Linear Systems with Random Inputs</font size>
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  • 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 properties
    19 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 ass
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  • *<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 is
    15 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 sha
    3 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 we
    18 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&lt;0, no samples can sit in x&lt;0 region. Th
    13 KB (1,966 words) - 10:50, 22 January 2015
  • [[Category:random variables]] Question 1: Probability and Random Processes
    4 KB (700 words) - 17:48, 13 March 2015
  • [[Category:random variables]] Question 1: Probability and Random Processes
    2 KB (331 words) - 17:37, 13 March 2015
  • [[Category:random variables]] Question 1: Probability and Random Processes
    3 KB (528 words) - 00:21, 10 March 2015
  • [[Category:random variables]] Question 1: Probability and Random Processes
    2 KB (384 words) - 00:22, 10 March 2015
  • 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 Processes
    6 KB (895 words) - 00:41, 10 March 2015
  • [[Category:random variables]] Question 1: Probability and Random Processes
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