• * [http://vise.www.ecn.purdue.edu/VISE/ee438L/lab1/pdf/lab1.pdf Lab on discrete and continuous signals] *[http://vise.www.ecn.purdue.edu/VISE/ee438L/lab2/pdf/lab2.pdf Lab on discrete-time systems]
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  • '''If X is discrete PX(k)''' = P(X<= k)-P(X<=k-1) * For Continuous Random Variable:
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  • ...r is denoted P(A|X = 0) and the latter P(A|X = 1). Now define a new random variable Y, whose value is P(A|X = 0) if X = 0 and P(A|X = 1) if X = 1. That is ...to be the conditional probability of the event A given the discrete random variable X:
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  • if X is a a positive random variable with small mean, it is unlikely to be very large Let X be a random variable such that X >= 0. <br>
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  • <math>p(X; \theta)</math> (discrete) <math>P(\theta)</math> (discrete)
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  • (Rosen - Discrete Mathematics and Its Appplications, 6th ed., pg. 440 (6.4.12)) ...ld roll the die any number of times from 1 to infinite. Consider a random variable R which is the number of rolls to roll a 6. We could determine the expecte
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  • ...dom variable" being observed should be the sum or mean of many independent random variables. (variables need not be iid)(See the PROOF ) ...nly statistical model that is needed is the conditional model of the class variable given the measurement. This conditional model can be obtained from a joint
    31 KB (4,832 words) - 17:13, 22 October 2010
  • ...real engineering. The concept of the Fourier Transform is extended to the discrete domain so that it may be computed using digital processors which is the bas ...weeks we spend on reviewing 301 material and spend more time on image and random process. -- [[User:xiao1|Yimin Xiao]]
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  • [[Category:discrete Fourier transform]] ...s (aka ''samples'') of a continuous-time function, <math>x(t)\,</math>, at discrete moments in time''':''' <math>t = nT\,</math>, where <math>T\,</math> is the
    13 KB (2,348 words) - 12:25, 2 December 2011
  • ...dom variable" being observed should be the sum or mean of many independent random variables. (variables need not be iid)(See the PROOF ) ...nly statistical model that is needed is the conditional model of the class variable given the measurement. This conditional model can be obtained from a joint
    31 KB (4,787 words) - 17:21, 22 October 2010
  • =='''1.4 Discrete Random Variables'''== ...cdots</math> are i.i.d. Bernoulli random variables, then Binomial random variable is defined as <math class="inline">\mathbf{X}=\mathbf{Y}_{1}+\mathbf{Y}_{2}
    5 KB (921 words) - 10:25, 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) - 10:47, 30 November 2010
  • ...a sequence of random variables that converge in mean square to the random variable <math class="inline">\mathbf{X}</math> . Does the sequence also converge to ...quence of random variable that converge in mean square sense to the random variable <math class="inline">\mathbf{X}</math> , also converges in probability to <
    6 KB (1,093 words) - 07:23, 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
    10 KB (1,608 words) - 07:31, 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}</math> . F
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  • =Example. Geometric random variable= Let <math class="inline">\mathbf{X}</math> be a random variable with probability mass function
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  • | Random variable | Discrete uniform
    6 KB (851 words) - 14:34, 23 April 2013
  • ...stem [[Video Tutorial on How to Cascade Transformations of the Independent Variable|cascade]]: <br>x(t) = the amount of protein released by damaged endothelium ...CT (computerized tomography) scans all convert analog physical signals to discrete computer signals. Systems (maybe even [[Fourier_Transform_Video |Fourier]]/
    17 KB (2,368 words) - 09:53, 6 May 2012
  • *Discrete Random Variables ...02S13Boutin|Normalizing the probability mass function of a discrete random variable]]
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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 (616 words) - 09:19, 13 September 2013
  • [[Category:random variables]] Question 1: Probability and Random Processes
    4 KB (572 words) - 09:24, 10 March 2015
  • Probability, Statistics, and Random Processes for Electrical Engineering, 3rd Edition, by Alberto Leon-Garcia, *Discrete Random Variables
    10 KB (1,422 words) - 19:14, 30 April 2013
  • ==Part 2: Discrete Random Variables (To be tested in the second intra-semestrial exam)== *2.2 Functions of a discrete random variable
    4 KB (498 words) - 09:18, 17 April 2013
  • ...short illustration of a research-level image processing problem for which discrete distributions are useful.
    2 KB (307 words) - 09:26, 4 February 2013
  • ...xamples. A formula for computing the expectation of a function of a random variable was also given. Along the way, we encountered the geometric series. Those w
    3 KB (341 words) - 08:59, 5 February 2013
  • ...iz in which you were asked to compute the Expectation of a discrete random variable. Twitter disrupted the lecture slightly, but I trust all of us will make a
    2 KB (335 words) - 12:00, 18 February 2013
  • ...dom variable does not change the variance, and that multiplying the random variable by a constant "a" has the effect of multiplying the variance by <math>a^2</
    2 KB (336 words) - 11:59, 18 February 2013
  • ...III of the material with a definition of the concept of "continuous random variable" along with two examples.
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  • [[Category:discrete random variable]] ...Problem]]: normalizing the probability mass function of a discrete random variable=
    2 KB (355 words) - 12:50, 13 February 2013
  • *On question 16 and 27, how do you deal with a infinite discrete random variable x? How do you calculate the probabilities with only known expected value? ...known, note that it is generally impossible to derive the pmf of a random variable only from its expected value. However, there is something remarkable about
    2 KB (302 words) - 09:52, 19 February 2013
  • ...at an example of continuous random variable, namely the exponential random variable.
    2 KB (329 words) - 07:16, 20 February 2013
  • In Lecture 19, we continued our discussion of continuous random variables. ...nvent a problem about the expectation and/or variable of a discrete random variable]]
    2 KB (252 words) - 07:20, 20 February 2013
  • ...us and discrete) and we began discussing normally distributed (continuous) random variables. ...02S13Boutin|Normalizing the probability mass function of a Gaussian random variable]]
    2 KB (304 words) - 06:43, 23 February 2013
  • ...a problem related to the expectation and/or variance of a discrete random variable and solve it. Then post your problem and solution on a Rhea page, and post [[Category:discrete random variable]]
    3 KB (467 words) - 17:17, 27 February 2013
  • ...gory:probability]] [[Category:problem solving]] [[Category:discrete random variable]] [[Category:expectation]] [[Category:variance]]
    4 KB (757 words) - 05:59, 22 February 2013
  • ...gory:probability]] [[Category:problem solving]] [[Category:discrete random variable]][[Category:expectation]] [[Category:variance]] ...vels from -2 V to 2 V with 1V difference. After the counter has sent out a random signal, each noise level has probability of {1/10,2/10,4/10,2/10,1/10}. The
    2 KB (299 words) - 17:13, 27 February 2013
  • ...iable. We also discussed the problem of recovering the pdf/pmf of a random variable from its moment generating function. ...CE302S13Boutin|Obtain the characteristic function of an exponential random variable]]
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  • ...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) - 06:02, 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 mentioned
    9 KB (1,507 words) - 15:23, 23 April 2013
  • Topic: Expectation of discrete random variable *Let X be a discrete random variable with probability mass function
    782 B (106 words) - 13:19, 25 April 2013
  • [[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) - 11:11, 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) - 11:11, 21 May 2014
  • [[ECE600_F13_rv_distribution_mhossain|Previous Topic: Random Variables: Distributions]]<br/> ...rv_Functions_of_random_variable_mhossain|Next Topic: Functions of a Random Variable]]
    6 KB (1,109 words) - 11:11, 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) - 11:11, 21 May 2014
  • ...unctions_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) - 11:12, 21 May 2014
  • [[ECE600_F13_notes_mhossain|'''The Comer Lectures on Random Variables and Signals''']] ...pdf f<math>_X</math> of a random variable X is a function of a real valued variable x. It is sometimes useful to work with a "frequency domain" representation
    5 KB (804 words) - 11:12, 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) - 11:12, 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. Th
    7 KB (1,307 words) - 11:12, 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) - 11:12, 21 May 2014

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