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- ='''1.11 Joint Characteristic Function'''= The joint characteristic function of two joint-distributed RVs <math class="inline">\mathbf{X}</math> and <m4 KB (711 words) - 11:32, 30 November 2010
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5 KB (803 words) - 12:10, 30 November 2010
- ...e Problem]]: Recover the probability mass function from the characteristic function = A discrete random variables X has a moment generating (characteristic) function <math>M_X(s)</math> such that1 KB (211 words) - 03:47, 27 March 2013
- ...:Category:Problem solving|Practice Problem]]: Obtain the moment generating function for an exponential random variable = Obtain the moment generating function <span class="texhtml">''M''<sub>''X''</sub>(''s'')</span> of X.2 KB (350 words) - 13:00, 27 March 2013
- = [[:Category:Problem solving|Practice Problem]]: PDF for a linear function of a random variable =2 KB (249 words) - 19:36, 27 March 2013
Page text matches
- Bayes' decision rule creates an objective function which minimizes the probability of error (misclassification). This method a Refers to the problem caused by exponential growth of hypervolume as a function of dimensionality. This term was coined by Richard Bellman in 1961.31 KB (4,832 words) - 18:13, 22 October 2010
- [[Lecture 13 - Kernel function for SVMs and ANNs introduction_Old Kiwi|13]], (Continued from [[Lecture 13 - Kernel function for SVMs and ANNs introduction_Old Kiwi]])13 KB (2,073 words) - 08:39, 17 January 2013
- ...t's simplify things. Each given differential equation can be written as a function of y. For instance, the differential equation ...d c. In this section, we are only considering differential equations whose characteristic equations have distinct, real roots. Let's call those roots r<sub>1</sub> a3 KB (527 words) - 18:10, 26 October 2009
- ...he Characteristic function of F_T(\omega) in a simple way (i.e. using prod function together with integrate). Other than that, I'll list the packages/functions ...st type “edit cov” in Matlab and then copy the whole function as a new function to your freemath program; I don’t know if it’s acceptable or not but of4 KB (596 words) - 13:17, 12 November 2010
- Bayes' decision rule creates an objective function which minimizes the probability of error (misclassification). This method a Refers to the problem caused by exponential growth of hypervolume as a function of dimensionality. This term was coined by Richard Bellman in 1961.31 KB (4,787 words) - 18:21, 22 October 2010
- According to the characteristic function of Poisson random variable3 KB (557 words) - 12:11, 25 September 2013
- ...ction)|CDF (Cumulative Distribution Function) and PDF (Probability Density Function)]] *[[ECE 600 Prerequisites Joint Characteristic Function|Joint Characteristic Function]]1 KB (139 words) - 13:13, 16 November 2010
- It is about the time until success in Poisson process. It has the characteristic of memoryless. Moment generating function5 KB (843 words) - 11:27, 30 November 2010
- 1.8.5 Characteristic function2 KB (305 words) - 11:15, 17 November 2010
- ='''1.11 Joint Characteristic Function'''= The joint characteristic function of two joint-distributed RVs <math class="inline">\mathbf{X}</math> and <m4 KB (711 words) - 11:32, 30 November 2010
- ...ass="inline">\mathbf{X}\left(t,\omega\right)</math> that is called sample function. ...="inline">\omega_{0}\in\mathcal{S}</math> is a function of time or sample function.16 KB (2,732 words) - 11:47, 30 November 2010
- ...c function)|Two jointly distributed random variables (Joint characteristic function)]]1 KB (188 words) - 11:57, 30 November 2010
- ...th> be a random variable with mean 2 , variance 8 , and moment generating function <math class="inline">\phi_{\mathbf{X}}\left(s\right)=E\left\{ e^{s\mathbf{X Find the characteristic function <math class="inline">\Phi\left(\omega\right)</math> of an exponentially di22 KB (3,780 words) - 07:18, 1 December 2010
- (a) Find the probability mass function (pmf) of <math class="inline">\mathbf{M}</math> . This is the characteristic function of Binomial with probability pr .12 KB (2,205 words) - 07:20, 1 December 2010
- ...e^{-A\left|x\right|}\text{ where }A>0.</math> Determine its characteristic function. ...If <math class="inline">R\left(\tau\right)</math> is the autocorrelation function of <math class="inline">\mathbf{X}\left(t\right)</math> , prove the followi7 KB (1,192 words) - 08:22, 27 June 2012
- Find the probability mass function (pmf) of <math class="inline">\mathbf{Z}</math> . Find the conditional probability mass function (pmf) of <math class="inline">\mathbf{X}</math> conditional on the event <10 KB (1,827 words) - 08:33, 27 June 2012
- ...he lower left corner of the unit square). Find the cumulative distribution function (cdf) <math class="inline">F_{\mathbf{X}}\left(x\right)=P\left(\left\{ \mat which is the characteristic function of a Gaussian random variable with mean <math class="inline">a\mu_{\mathbf{10 KB (1,652 words) - 08:32, 27 June 2012
- ...class="inline">\left|\rho\right|<1</math> . Find the joint characteristic function <math class="inline">E\left[e^{i\left(h_{1}\mathbf{X}+h_{2}\mathbf{Y}\right • Now, we can get the joint characteristic function <math class="inline">\Phi_{\mathbf{X}\mathbf{Y}}\left(\omega_{1},\omega_{2}6 KB (916 words) - 08:26, 27 June 2012
- Find the probability density function of <math class="inline">\mathbf{Y}=\max\left\{ \mathbf{X}_{1},\cdots,\mathb Find the probability density function of <math class="inline">\mathbf{Z}=\min\left\{ \mathbf{X}_{1},\cdots,\mathb14 KB (2,358 words) - 08:31, 27 June 2012
- ...X}</math> is a binomial distributed random variable with probability mass function (pmf) given by <math class="inline">p_{n}\left(k\right)=\left(\begin{array} ...line">\mathbf{X}</math> . (You must show how you derive the characteristic function.)10 KB (1,754 words) - 08:30, 27 June 2012
- Find the characteristic function of <math class="inline">\mathbf{X}_{n}</math> . ...t(1-\left(\frac{1}{2}\right)^{2n}\right)</math> . Hence the characteristic function of <math class="inline">\mathbf{X}_{n}</math> is <math class="inline">\Phi14 KB (2,439 words) - 08:29, 27 June 2012
- ...function <math class="inline">\mu\left(t\right)</math> and autocovariance function <math class="inline">C_{\mathbf{XX}}\left(t_{1},t_{2}\right)</math> . ...expression for the <math class="inline">n</math> -th order characteristic function of <math class="inline">\mathbf{X}\left(t\right)</math> in terms of <math10 KB (1,636 words) - 08:29, 27 June 2012
- According to the characteristic function of Poisson random variable3 KB (532 words) - 11:58, 30 November 2010
- ...hbf{Z}</math> is a Guassian random variable, then it has a characteristic function of the form ...XY}}\left(\omega_{1},\omega_{2}\right)</math> is the joint characteristic function of <math class="inline">\mathbf{X}</math> and <math class="inline">\mathbf3 KB (504 words) - 12:00, 30 November 2010
- ...ass="inline">\mathbf{X}</math> be a random variable with probability mass function (a) Find the characteristic function of <math class="inline">\mathbf{X}</math> .5 KB (793 words) - 12:10, 30 November 2010
- ...}</math> as <math>n\rightarrow\infty</math> , which is the characteristic function of a Poisson random variable with mean <math>\lambda</math> . which is the characteristic function of Poisson random variable with mean <math>\lambda</math> .3 KB (470 words) - 13:02, 23 November 2010
- ...ath class="inline">n\rightarrow\infty</math> , which is the characteristic function of a Poisson random variable with mean <math class="inline">\lambda</math> which is the characteristic function of Poisson random variable with mean <math class="inline">\lambda</math> .3 KB (539 words) - 12:14, 30 November 2010
- ...sequence of i.i.d. Gaussian random variables, each having characteristic function • Probability generating function of <math class="inline">\mathbf{N}</math> is <math class="inline">P_{\math2 KB (426 words) - 07:15, 1 December 2010
- | Probability density function <math> f_{x}(x) </math> | Characteristic function <math> \Phi_{x}(\omega)</math>6 KB (851 words) - 15:34, 23 April 2013
- ...probability_normalization_ECE302S13Boutin|Normalizing the probability mass function of a discrete random variable]] ...on_gaussian_normalization_ECE302S13Boutin|Normalizing the probability mass function of a Gaussian random variable]]7 KB (960 words) - 18:17, 23 February 2015
- [[Lecture 13 - Kernel function for SVMs and ANNs introduction_OldKiwi|13]]| (Continued from [[Lecture 13 - Kernel function for SVMs and ANNs introduction_OldKiwi|Lecture 13]])13 KB (2,098 words) - 11:21, 10 June 2013
- ...e^{-A\left|x\right|}\text{ where }A>0.</math> Determine its characteristic function. ...If <math class="inline">R\left(\tau\right)</math> is the autocorrelation function of <math class="inline">\mathbf{X}\left(t\right)</math> , prove the followi3 KB (406 words) - 10:19, 13 September 2013
- ...function <math class="inline">\mu\left(t\right)</math> and autocovariance function <math class="inline">C_{\mathbf{XX}}\left(t_{1},t_{2}\right)</math> . ...expression for the <math class="inline">n</math> -th order characteristic function of <math class="inline">\mathbf{X}\left(t\right)</math> in terms of <math5 KB (763 words) - 10:57, 10 March 2015
- '''(a)''' Find the probability mass function (pmf) of <math class="inline">\mathbf{Z}</math> . '''(b)''' Find the conditional probability mass function (pmf) of <math class="inline">\mathbf{X}</math> conditional on the event <5 KB (780 words) - 01:25, 9 March 2015
- Find the probability density function of <math class="inline">\mathbf{Y}=\max\left\{ \mathbf{X}_{1},\cdots,\mathb Find the probability density function of <math class="inline">\mathbf{Z}=\min\left\{ \mathbf{X}_{1},\cdots,\mathb5 KB (735 words) - 01:17, 10 March 2015
- ...X}</math> is a binomial distributed random variable with probability mass function (pmf) given by <math class="inline">p_{n}\left(k\right)=\left(\begin{array} ...line">\mathbf{X}</math> . (You must show how you derive the characteristic function.)4 KB (609 words) - 01:54, 10 March 2015
- Find the characteristic function of <math class="inline">\mathbf{X}_{n}</math> . ...">\Phi</math> be the standard normal distribution, i.e., the distribution function of a zero-mean, unit-variance Gaussian random variable. Let <math class="in5 KB (726 words) - 10:35, 10 March 2015
- ...e^{-A\left|x\right|}\text{ where }A>0.</math> Determine its characteristic function.2 KB (358 words) - 10:33, 13 September 2013
- ...lass="inline">\mathbf{X}_{n}</math> 's are i.i.d. RVs with characteristic function given by <math class="inline">\Phi_{\mathbf{X}}\left(\omega\right)=\frac{1} '''(a)''' Determine the characteristic function of <math class="inline">\mathbf{Z}</math> .2 KB (282 words) - 10:34, 13 September 2013
- ...olor{blue}\left( \text{a} \right) \text{Find the joint probability density function } f_{YZ}(y,z).</math>'''<br> ...ero-mean continuous-time Gaussian white noise process with autocorrelation function4 KB (547 words) - 16:40, 30 March 2015
- ...ut discretization of ''atan'' is not quite as straightforward. The atan() function you might normally invoke from the <math.h> library requires floating ...rom the following image. Also note how the characteristic of the ''atan'' function can be seen in the frequency trend of LUT values.8 KB (1,176 words) - 15:15, 1 May 2016
- ...probability_normalization_ECE302S13Boutin|Normalizing the probability mass function of a discrete random variable]] ...on_gaussian_normalization_ECE302S13Boutin|Normalizing the probability mass function of a Gaussian random variable]]10 KB (1,422 words) - 20:14, 30 April 2013
- *3.1 Definition of continuous random variable, probability density function. *3.3 The cumulative distribution function of a random variable (discrete or continuous)4 KB (498 words) - 10:18, 17 April 2013
- ...of recovering the pdf/pmf of a random variable from its moment generating function. ...ction_ECE302S13Boutin|Recover the pmf corresponding to this characteristic function]]2 KB (336 words) - 09:39, 18 March 2013
- ...d_conditional_pdf_ECE302S13Boutin|Find the conditional probability density function]] ...nditional_ellipse_ECE302S13Boutin|Find the conditional probability density function (again)]]2 KB (340 words) - 03:37, 27 March 2013
- ...e Problem]]: Recover the probability mass function from the characteristic function = A discrete random variables X has a moment generating (characteristic) function <math>M_X(s)</math> such that1 KB (211 words) - 03:47, 27 March 2013
- Find the conditional probability density function for some constants a,b>0. Find the conditional probability density function <math>f_{X|Y}(x|y).</math>3 KB (559 words) - 07:02, 22 March 2013
- ...d_conditional_pdf_ECE302S13Boutin|Find the conditional probability density function]] ...nditional_ellipse_ECE302S13Boutin|Find the conditional probability density function (again)]]2 KB (333 words) - 18:02, 2 April 2013
- ...e you that lambda =3 hint so that you can factor out a (lambda-3) from the characteristic polynomial and find the other two roots via the quadratic formula. Now I th Also with Question 6 I am getting a very nasty looking characteristic equation, so I am not to sure how to solve for the algebraic roots.17 KB (2,975 words) - 12:36, 11 September 2013
- [[ECE600_F13_Characteristic_Functions_mhossain|Next Topic: Characteristic Functions]] ...random variable X using the density function f<math>_X</math> or the mass function p<math>_X</math>. <br/>8 KB (1,474 words) - 12:12, 21 May 2014
- <font size= 3> Topic 10: Characteristic Functions</font size> ==Characteristic Functions==5 KB (804 words) - 12:12, 21 May 2014
- ...expectation E[g(X)], conditional expectation E[g(X)|M], and characteristic function <math>\Phi_X</math>. We will now define similar tools for the case of two r ==Joint Cumulative Distribution Function==8 KB (1,524 words) - 12:12, 21 May 2014
- which is a quadratic function of a ∈ '''R'''. Consider two cases: We have previously seen that the joint density function for Gaussian X and Y contains a parameter r. It can be shown that this r is7 KB (1,307 words) - 12:12, 21 May 2014
- ...sson|Ryan Russon]]: I guess what I am confused about is how I can take the function ''f(x)'' and let ''x''--> ''x+ct'' and ''x-ct'' and then from that, I get t ...lly are getting the superposition of the odd extensions of each 1/2 of the function of x but as it is shifted through time, which in turn just shifts the ''f(x6 KB (1,102 words) - 19:16, 19 November 2013
- * The cumulative distribution function of <span style="text-decoration:underline;">X</span> is <br/> : and the probability density function of <span style="text-decoration:underline;">X</span> is <br/>12 KB (1,897 words) - 12:13, 21 May 2014
- * X(t,<math>\omega_0</math>) is a real-valued function of t for fixed <math>\omega_0</math>. '''Definition''' <math>\qquad</math> The '''autocorrelation function''' of a random process X(t) is <br>10 KB (1,690 words) - 12:13, 21 May 2014
- ...uler's characteristic: X = V - E + F. Any convex polyhedra's surface has a characteristic X = 2, which all five of the Platonic Solids do. ...composition (the application of one function to another to produce a third function) as its operation. Every rotation within the SO(3) group, also has an inver9 KB (1,540 words) - 10:36, 2 December 2013
- Neyman-Pearson Lemma and Receiver Operating Characteristic Curve ...this slecture is understanding Neyman-Pearson Lemma and Receiver Operating Characteristic (ROC) curve from theory to application. The fundamental theories stem from15 KB (2,306 words) - 10:48, 22 January 2015
- According to Euler Characteristic, any convex polyhedron's surface has Euler characteristic E+2=V+F.<br> •Let me use one example to illustrate my understanding of Euler characteristic:<br><br>5 KB (911 words) - 11:27, 27 April 2014
- ''Receiver Operating Characteristic (ROC)'' curve is often used as an important tool to visualize the performan And we use a binary decision rule <math>\ \phi(x)\ </math> as a function:11 KB (1,823 words) - 10:48, 22 January 2015
- (a) Find the (first order) characteristic function of <math class="inline">\mathbf{X}\left(t\right)</math> . (c) Derive an expression for the autocorrelation function of <math class="inline">\mathbf{X}\left(t\right)</math> .4 KB (700 words) - 17:48, 13 March 2015
- which is the characteristic function of a Gaussian random variable with mean <math class="inline">a\mu_{\mathbf{3 KB (525 words) - 00:20, 10 March 2015
- ...class="inline">\left|\rho\right|<1</math> . Find the joint characteristic function <math class="inline">E\left[e^{i\left(h_{1}\mathbf{X}+h_{2}\mathbf{Y}\right Use the fact that the characteristic function of a <math class="inline">N\left(0,1\right)</math> r.v. is given by <math6 KB (895 words) - 00:41, 10 March 2015
- ...math> where <math class="inline">u\left(t\right)</math> is the unit step function and <math class="inline">T>0</math> . What is the autocorrelation function of <math class="inline">\mathbf{Y}\left(t\right)</math> ?6 KB (1,002 words) - 01:38, 10 March 2015
- ...X}</math> is a binomial distributed random variable with probability mass function (pmf) given by <math class="inline">p_{n}\left(k\right)=\left(\begin{array} ...line">\mathbf{X}</math> . (You must show how you derive the characteristic function.)4 KB (758 words) - 01:56, 10 March 2015
- ..., with <math class="inline">\mathbf{X}_{n}</math> having probability mass function <math class="inline">p_{n}\left(k\right)=\left(\begin{array}{c} ...nline">e^{\lambda\left(e^{i\omega}-1\right)}</math> is the characteristic function of a Poisson random variable with mean <math class="inline">\lambda</math>3 KB (429 words) - 01:57, 10 March 2015
- Find the characteristic function of <math class="inline">\mathbf{X}_{n}</math> . ...t(1-\left(\frac{1}{2}\right)^{2n}\right)</math> . Hence the characteristic function of <math class="inline">\mathbf{X}_{n}</math> is <math class="inline">\Phi4 KB (692 words) - 10:36, 10 March 2015
- ...function <math class="inline">\mu\left(t\right)</math> and autocovariance function <math class="inline">C_{\mathbf{XX}}\left(t_{1},t_{2}\right)</math> . ...expression for the <math class="inline">n</math> -th order characteristic function of <math class="inline">\mathbf{X}\left(t\right)</math> in terms of <math3 KB (451 words) - 10:56, 10 March 2015
- ...nverge in distribution]]. Furthermore, you have to know the characteristic function of Cauchy distributed random varaible. According to the characteristic function of Cauchy distributed random variable,3 KB (451 words) - 10:58, 10 March 2015
- Then, compute the characteristic function of <math>\mathbf{X}+\mathbf{Y}</math>: We know that the characteristic function of a Gaussian random variable with mean <math>\mu</math> and variance <math5 KB (882 words) - 01:54, 31 March 2015
- ...ero-mean continuous-time Gaussian white noise process with autocorrelation function ...ath> whose Fourier transform <math>H(\omega)</math> has the ideal low-pass characteristic8 KB (1,336 words) - 01:53, 31 March 2015
- ...th> and <math>\lambda_2</math>, calculate the conditional probability mass function of <math>X</math> given that <math>X+Y=n</math>. ...ntial random variables with mean <math>\mu</math>. Find the characteristic function of <math>X+Y</math>.2 KB (351 words) - 00:17, 4 December 2015
- ...y independent random variables <math>X</math> and <math>Y</math> and their characteristic functions <math>\phi_X(\omega),\,\phi_Y(\omega)</math> we have the followin 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
- Characteristic Analysis of a Simple Distortion Pedal With the help of Matlab, I obtained frequency responses for both transfer function: (with the Tone button turn to leftmost position and to the rightmost posit5 KB (752 words) - 16:44, 2 December 2017
- Characteristic Analysis of a Simple Distortion Pedal (incomplete yet) With the help of Matlab, I obtained frequency responses for both transfer function: (with the Tone button turn to leftmost position and to the rightmost posit3 KB (499 words) - 03:53, 2 December 2017
- ...es. This characteristic is called self-similarity, which is the best-known characteristic of a fractal. This concept isn't new at all. In fact, artists and crafters ...ince they can all be transformed into another. Going back to fractals, the characteristic of having a fractal dimension greater than its topological dimension is tru24 KB (3,663 words) - 01:01, 7 December 2020
- ...rate, aperiodic tiling contains only non-periodic tiling. This is a unique characteristic of Penrose tiling. Reflection symmetry is a characteristic that an image possesses when one half of the image is the reflection of the6 KB (902 words) - 01:51, 6 December 2020
- ...one know it is a group? What is its operation? A Galois group makes use of function composition as its operation, f * g, where f and g are members of the Galoi ...group over the radicals. The Abel-Ruffini theorem is valid for fields of "characteristic 0." This is a condition that may be ignored for the purposes of this articl7 KB (1,274 words) - 00:51, 7 December 2020
