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- ...the Chernoff distance in the case of Normally distributed data. In section 3.2, some examples for the Chernoff bound are provided. ...\Re Prob \big(error \mid x\big) \rho \big(x\big) dx \text{......Eq.(2.3)}17 KB (2,590 words) - 10:45, 22 January 2015
- \begin{cases} \end{cases} </math>29 KB (4,474 words) - 13:58, 22 May 2015
- |<math> \sin x \ = \ x \ - \ \frac{x^3}{3!} \ + \ \frac{x^5}{5!} \ - \ \frac{x^7}{7!} \ + \ \cdots, \quad \text{ for ...+ \binom{n}{1} a^{n-1}x + \binom{n}{2} a^{n-2}x^2 + \binom{n}{3} a^{n-3}x^3 + \ldots + x^n \\15 KB (2,182 words) - 18:14, 27 February 2015
- There are four cases that arise which one must consider: <b> Case 3 </b>: Denominator contains irreducible quadratic factors, none of which is4 KB (602 words) - 13:49, 3 March 2015
- \begin{cases} \end{cases} </math>8 KB (1,517 words) - 17:56, 26 February 2015
- '''3. (30 Points)''' <math class="inline">cov\left(\mathbf{X}_{j},\mathbf{X}_{k}\right)=\begin{cases}5 KB (928 words) - 17:46, 13 March 2015
- ! style="background: none repeat scroll 0% 0% rgb(238, 238, 238);" colspan="3" | (double-sided) [[info_z-transform|Z Transform]] and its Inverse \begin{cases}7 KB (1,018 words) - 08:55, 6 March 2015
- &= \begin{cases} \frac{1}{1-\frac{1}{z}}, & |z| > 1 \\ diverges, & else \end{cases} === Answer 3 ===3 KB (431 words) - 09:09, 4 March 2015
- '''Part 3.''' '''3. (30 Points)'''5 KB (780 words) - 01:25, 9 March 2015
- '''Part 3.''' 25 pts ...E-QE_CS1-2011_solusion-3|here]] to view student [[ECE-QE_CS1-2011_solusion-3|answers and discussions]]'''4 KB (547 words) - 16:40, 30 March 2015
- 3. \text{ Multiply step 2 by the filter } H(\rho) = |\rho| = f_c \left [ rect 4. \text{ Compute inverseFT of step 3.}17 KB (2,783 words) - 01:51, 31 March 2015
- Fig. 3 ...rious if such a configuration was possible. Observing that there are only 3 binary variables, a binary table can be constructed by consulting the sign3 KB (474 words) - 15:17, 1 May 2016
- ...he elements of the output vector and '''x<sub>1</sub>,x<sub>2</sub>, x<sub>3</sub>''' ... are each of the elements of the input vector. ==== Example #3: ====18 KB (2,894 words) - 12:17, 3 March 2015
- '''Problem 3.''' 25 pts <math class="inline">f_{X}\left(x\right)=\begin{cases}3 KB (449 words) - 21:36, 5 August 2018
- ...und''' is one such upper bound which is reasonably easy to compute in many cases. Therefore we will present this bound, and then discuss a few results that ...math> belongs in class <math> 1 </math>, and vise versa. Although, in many cases calculating <math>\rho(\omega_i | x)</math> is impossible, or extremely dif13 KB (2,062 words) - 10:45, 22 January 2015
- ...e classification task with examples, and how we can derive it in different cases. The following sections describe two cases of classification. One is where data exist in 1-dimensional feature space a19 KB (3,255 words) - 10:47, 22 January 2015
- ==Part 3: Examples of MLE (Analytically Tractable Cases)== ...3-statistics-for-applications-fall-2006/lecture-notes/lecture3.pdf Lecture 3: Properties of MLE: consistency, asymptotic normality. Fisher information],3 KB (427 words) - 10:50, 22 January 2015
- ...r>the following probability mass functions for each of the above mentioned cases:'''<br>''' <math>Pr(H = 49 | p = {1}/{3}) = \binom{80}{49}(1/3)^{49}(1 - 1/3)^31 \approx 0.000</math><br>25 KB (4,187 words) - 10:49, 22 January 2015
- Then we provide examples for the cases of 1D and 2D features, and we derive Bayes rule for minimizing risk in these cases.12 KB (1,810 words) - 10:46, 22 January 2015
- ...timation states that, for N Observations x<sub>1</sub>,x<sub>2</sub>,x<sub>3</sub>,...,x<sub>n</sub> the density at a point x<sub>0</sub> can be approxi The above claim is true only in cases where the window function <math>\phi</math> defines a region R with well de10 KB (1,743 words) - 10:54, 22 January 2015
- [[Category:3 Cases]] ...i)-\frac{d}{2} \ln 2\pi -\frac{1}{2}\ln |\mathbf{\Sigma}_i|+\ln P(w_i)~~~~(3)14 KB (2,287 words) - 10:46, 22 January 2015
- ...guarantee that sufficient number of samples are used for training. In some cases, small sample sizes could lead to an accidental characteristics where it wi ...) \geq D(\vec{x_{1}},\vec{x_{3}}), \forall \vec{x_{1}},\vec{x_{2}},\vec{x_{3}} \in S</math>14 KB (2,313 words) - 10:55, 22 January 2015
- ...ocally estimate density function by a small number of neighboring samples [3] and therefore show less accurate estimation results. In spite of their acc and displayed in Figure 1(a) and 1(b) below such cases where <math>d</math> = 1 and <math>d</math> = 2, respectively.11 KB (1,824 words) - 10:53, 22 January 2015
- In both cases, it seems that one could be well-served to try to construct a p.d.f. based ...p(\vec{X})</math> goes to infinity as ''V'' goes to zero. Neither of these cases is helpful in our search for the true <math>p(\vec{X})</math>.16 KB (2,703 words) - 10:54, 22 January 2015
- <br> In most cases when n>p, it is impossible to find a solution for <math>\textbf{c}</math ...above three kernel functions. The classfications are illustrated in Fig.1~3. The parameters are tuned by cross-validation. The mis-classification rates14 KB (2,241 words) - 10:56, 22 January 2015
- == ''' 3. A quick example about ROC in binary classification'''<sup>'''[2] '''< ...e are 3 records in class ''C1'' and 3 in ''C2'', i.e.''P'' = 3 and ''N'' = 3. Column 4 - 7 gives the records counts with the threshold value''t'' set to11 KB (1,823 words) - 10:48, 22 January 2015
- <math>\phi(x) = \rho(x_1,x_2,...,x_n) = \begin{cases} \end{cases}</math>12 KB (2,086 words) - 10:54, 22 January 2015
- \begin{cases} \end{cases}9 KB (1,540 words) - 10:56, 22 January 2015
- * Derivation of Bayes' rule in discrete and continuous cases. ...will consider the derivation of Bayes rule both in discrete and continues cases.7 KB (1,106 words) - 10:42, 22 January 2015
- ...h>\theta</math> may occur, and needs to guarantee good performance for all cases, then the ML estimator is usually a good choice. =Example 3: pD Gaussuan, <math>(\mu,R)</math> unknown=19 KB (3,418 words) - 10:50, 22 January 2015
- === <br> 3. Practice considerations === ==== 3.1 Log-likelihood ====13 KB (1,966 words) - 10:50, 22 January 2015
- <center>[[Image:runyan3.jpg|frame|none|alt=Alt text|<font size= 4> '''Figure 3''' </font size>]] </center> <br /> # Repeat steps 2 and 3 until the value of <math>J</math> no longer changes8 KB (1,350 words) - 10:57, 22 January 2015
- \begin{cases} \end{cases}5 KB (790 words) - 10:01, 14 March 2015
- <font size = 3>The purpose of Upsampling is to manipulate a signal in order to artificiall <font size = 3>3 KB (565 words) - 10:01, 14 March 2015
- ...solely on the 'r' value that is contained in 'z'. The ROC is one of three cases; :3. The ROC is the space in between two circles centered at the origin.6 KB (1,019 words) - 18:11, 23 February 2015
- =QE2013_AC-3_ECE580-3= ...3_AC-3_ECE580-1|Part 1]],[[QE2013_AC-3_ECE580-2|2]],[[QE2013_AC-3_ECE580-3|3]],[[QE2013_AC-3_ECE580-4|4]],[[QE2013_AC-3_ECE580-5|5]]8 KB (1,016 words) - 12:19, 25 March 2015
- ...3_AC-3_ECE580-1|Part 1]],[[QE2013_AC-3_ECE580-2|2]],[[QE2013_AC-3_ECE580-3|3]],[[QE2013_AC-3_ECE580-4|4]],[[QE2013_AC-3_ECE580-5|5]] ...iplier approach, which is more complicated but would apply to more general cases. Solution 1 is not as general but is simpler for the given problem. They2 KB (330 words) - 12:22, 25 March 2015
- | <math> \int x^{2} ch ax dx=(\dfrac{x^{2}}{a^{2}}+\dfrac{2}{a^{3}}) sh ax-\dfrac{2x}{a^{2}} ch ax +C</math> ...int\dfrac{dx}{(ch ax+1)^{2}}=\dfrac{1}{2a}th\dfrac{ax}{2}-\dfrac{1}{6a}th^{3}\dfrac{ax}{2} +C</math>8 KB (1,479 words) - 17:44, 26 February 2015
- | <math> \int\arg ch\dfrac{a}{x}dx=\begin{cases} ...{x}+\arcsin\dfrac{x}{a}}{x\arg ch\dfrac{a}{x}-\arcsin\dfrac{x}{a}} & .\end{cases} +C</math>3 KB (624 words) - 17:52, 26 February 2015
- |<math> \int x^2 \arcsin \frac {x }{ a}dx = \frac{x^3}{3}\arcsin \frac {x}{a} + \frac {\left( x^2+2a^2 \right) \sqrt { a^2-x^2 }}{9} ...ot 3}+ \frac{1 \cdot 3(x/a)^5}{2 \cdot 4 \cdot 5 \cdot 5} + \frac {1 \cdot 3 \cdot 5 (x/a)^7}{2 \cdot 4 \cdot 6 \cdot 7 \cdot 7} + \cdot \cdot \cdot +C<8 KB (1,433 words) - 17:05, 26 February 2015
- ...rac {ax}{1 \cdot 1!} + \frac {(ax)^2}{2 \cdot 2!} + \frac {(ax)^3}{3 \cdot 3!} + \cdot \cdot \cdot +C</math> \begin{cases}3 KB (513 words) - 17:09, 26 February 2015
- | <math> \int x^{2} sh ax dx=(\dfrac{x^{2}}{a^{2}}+\dfrac{2}{a^{3}}) ch ax-\dfrac{2x}{a^{2}} sh ax +C</math> | <math> \int\dfrac{sh ax}{x} dx=ax+\dfrac{(ax)^{3}}{3\cdot3!}+\dfrac{(ax)^{5}}{5\cdot5!}+\cdots +C</math>7 KB (1,378 words) - 17:42, 26 February 2015
- \begin{cases} \end{cases} </math>4 KB (826 words) - 18:06, 26 February 2015
- ...{ ax + b} = \frac {(ax+b)^2}{2a^3} - \frac {2b(ax+b) }{a^3} + \frac{b^2}{a^3} \ln (ax +b)+C</math> ...{3a^4} - \frac {3b(ax+b)^2 }{2a^4} + \frac{3b^2(ax+b)}{a^4} - \frac{b^3}{a^3}\ln (ax +b)+C</math>7 KB (1,373 words) - 18:07, 26 February 2015
- ...h> \int x^2 \sin a x d x = \frac {2 x}{a^2} \sin a x + \left ( \frac {2}{a^3} - \frac {x^2}{a} \right)\cos a x +C</math> ...}{a^2} - \frac{6}{a^4}\right)\sin a x + \left ( \frac {6x}{a^3} - \frac {x^3}{a} \right)\cos a x +C</math>14 KB (2,809 words) - 16:12, 26 February 2015
- ...that the distribution of stars within a galaxy is accurately modeled by a 3-dimensional homogeneous Poisson process for which the following two facts a ...ius }r\right\} \right)</math><math class="inline">=1-e^{-\frac{4}{3}\pi r^{3}\lambda}.</math>2 KB (384 words) - 00:22, 10 March 2015
- ...ing i.i.d , <math class="inline">\mathbf{X}_{1},\mathbf{X}_{2},\mathbf{X}_{3},\cdots</math> each have finite mean <math class="inline">\mu</math> , and <math class="inline">E\left[\mathbf{X}_{i}\mathbf{X}_{j}\right]=\begin{cases}4 KB (699 words) - 11:08, 10 March 2015
- \begin{cases} \end{cases} </math>29 KB (4,417 words) - 15:53, 12 March 2015
- ...n-1|Part 1]],[[ECE-QE_CS1-2011_solusion-2|2]],[[ECE-QE_CS1-2011_solusion-3|3]] \begin{cases}8 KB (1,336 words) - 01:53, 31 March 2015
- =[[HW3ECE38F15|Homework 3]] Solution, [[ECE438]], [[2015_Fall_ECE_438_Boutin|Fall 2015]], [[user:mbou ==Question 3==7 KB (1,181 words) - 19:17, 19 October 2015
- ...X_5[0]e^{j2\pi n0/5} + X_5[1]e^{j2\pi n1/5} + X_5[2]e^{j2\pi n2/5} + X_5[3]e^{j2\pi n3/5} + X_5[4]e^{j2\pi n4/5} \right ) \\ X_5[1]=5 \mbox{, and } X_5[0]=X_5[2]=X_5[3]=X_5[4]=09 KB (1,594 words) - 15:36, 20 October 2015
- \mathcal{Y}(\omega) =\frac{1}{4} \sum_{k=0}^{3} \mathcal{X} \left (\frac{\omega-k2\pi}{4} \right ) ==Question 3==6 KB (945 words) - 11:40, 19 October 2015
- ...modeled as an impulse train passing through the vocal tract. While in both cases vocal tract selects the noise heard, in voiced sound the impulse train dete ...ally eliminated almost completely. Since the noise is not periodic in most cases, any substantial noise is effectively multiplied by a zero. The probability9 KB (1,777 words) - 23:23, 21 November 2015
- \begin{cases} \end{cases}5 KB (766 words) - 22:18, 7 March 2016
- <math> f(d) = 3 </math> <br /> * Analysis of social structures (special cases may include schools, military, parties, events, etc.).13 KB (2,051 words) - 22:06, 24 April 2016
- *In some cases, we need pre-processing to transform the data in some way to get the statis ==3. algorithm assumption==8 KB (1,405 words) - 22:56, 27 November 2016
- ...essed signals. In this project, I want to explore what will happen in both cases. In order to feel it more directly, I decided to process some music signals ==3. Result==3 KB (553 words) - 22:41, 26 November 2016
- \bar{E}=\begin{cases} \end{cases}} \left(\frac{V}{m}\right)4 KB (646 words) - 23:24, 25 April 2017
- <math>\quad rank=2\ne \mbox 3</math> \qquad rank<3 \qquad must\;contain\;\lambda=-14 KB (588 words) - 00:10, 21 May 2017
- <math>\begin{cases} \end{cases}</math>4 KB (557 words) - 01:01, 21 May 2017
- <math>\begin{cases} \end{cases}</math>7 KB (1,126 words) - 05:45, 22 May 2017
- <math>\begin{cases} \end{cases}</math>3 KB (393 words) - 11:33, 18 June 2017
- & = \begin{cases}Ar\cos\theta, r<a \hspace{3cm} \leftarrow\text{ no singularity at }r=0\\ \end{cases}4 KB (702 words) - 17:02, 17 June 2017
- ...{2cm}r\le a\\-E_0r\cos\theta+\frac{B\cos\theta}{r^2}\hspace{2cm}r\ge a\end{cases} <math>Aa = -E_0a+\frac{B}{a^2}\to A = -E_0 + \frac{B}{a^3}</math>4 KB (642 words) - 10:44, 18 June 2017
- ...ega}\bigg)\\\sigma\to\infty\to\epsilon_c\to\infty\\\text{ then }M_c=0 \end{cases}</math> 3) <math>\nabla\times\bar{H} = \bar{J}+\frac{\partial D}{\partial t}\hspace{13 KB (591 words) - 11:21, 18 June 2017
- ...ega}\bigg)\\\sigma\to\infty\to\epsilon_c\to\infty\\\text{ then }M_c=0 \end{cases}</math> 3) <math>\nabla\times\bar{H} = \bar{J}+\frac{\partial D}{\partial t}\hspace{13 KB (591 words) - 11:24, 18 June 2017
- \rho=\begin{cases} qN_{D2} & x_{n1}\le x\le x_{n2}\text{ region 3}\\2 KB (385 words) - 10:52, 6 August 2017
- In both cases ‘R’ refers to the radius if the graph were to be revolved around the gi ==3. References==3 KB (576 words) - 20:37, 3 October 2017
- In both cases ‘'''<math>R</math>'''’ refers to the "'''radius'''" if the graph were t ==3. References==4 KB (664 words) - 09:42, 19 January 2018
- <math>=\begin{cases} undefined, & if & s≤2 \end{cases} </math>.6 KB (1,071 words) - 18:26, 22 November 2017
- ...ac{dx}{dt}}{t} - \frac{x}{t^2}</math>, <math>\frac{d^2y}{dt^2}=\frac{2x}{t^3} - \frac{2\frac{dx}{dt}}{t^2} + \frac{\frac{d^2y}{dt^2}}{t}</math>. Substitute them into ODE, hence <math>t^2 (lnt+1) (\frac{2x}{t^3} - \frac{2\frac{dx}{dt}}{t^2} + \frac{\frac{d^2x}{dt^2}}{t}) + t (2lnt+1) (7 KB (1,254 words) - 19:49, 22 November 2017
- <math>y(t)=\begin{cases} \end{cases}</math><br />5 KB (985 words) - 12:38, 30 November 2018
- <small>''Figure 3 Merma, 2004 P80 The logistic equation Adapted from Northwestern University The following graph demonstrates four different cases with θ>1 or θ<1.10 KB (1,532 words) - 22:51, 2 December 2018
- Question 3: Optimization6 KB (899 words) - 01:04, 24 February 2019
- ...ve all permutations pertaining to who draws which name and determine which cases will have every person draw someone else's name. ...ginal" spot. These two permutations are called derangements of <math>\{1,2,3\}</math>.6 KB (996 words) - 00:53, 3 December 2018
- ...ta^2(n+5)^2]}+\dfrac{sin[(1-\beta)\pi(n+0.5)/2]}{\pi[(n+.5)-4\beta^2(n+.5)^3]},-\infty<n<\infty</math> with <math>\beta=0.5</math> <br> \begin{cases}4 KB (738 words) - 15:34, 19 February 2019
- Question 3: Optimization <math>\begin{cases}1 KB (178 words) - 11:45, 25 February 2019
- Question 3: Optimization Subject to <math>x_1+x_2-2<=0</math> and <math>x_1+2x_2-3<=0</math><br>2 KB (247 words) - 11:48, 25 February 2019
- \begin{cases} \end{cases}1 KB (190 words) - 16:32, 19 February 2019
- [[File:windowSmall.png|400px|thumb|right|Filtered Image using LPF (Window = 3 pixels)]] B = imData(:,:,3);7 KB (1,006 words) - 19:22, 7 April 2019
- ...signal will be a Double Sided modulation that carries audio files 1, 2 and 3. You remember this at a cosine carrier from class. The second radio signal Radio Signal 1 will carry file 1 at 1000Hz, file 2 at 4000Hz, and file 3 at 7000.1 KB (185 words) - 17:30, 25 April 2019
- <math>2𝜋T_1f_{max} < \frac{𝜋}{D}</math> (3) ...want to send them the “Happy Birthday” song which has <math>f_{max} = 3,000</math> Hz. As before, the scientists would like to downsample the song16 KB (2,611 words) - 14:11, 12 November 2019
- ===3. Formula Visualization=== ...und this circle at a certain frequency. For example, let <math>g(t) = \sin(3*2\pi t) + 1</math> (graph pictured below). To wrap ''g(t)'' around the circ12 KB (2,051 words) - 14:20, 5 December 2020
- | [[Walther_MA271_Fall2020_topic12#3.0 Elliptical Curves and Fields|3.0 Elliptical Curves and Fields]] ...= x<sup>3</sup> + Ax + B with distinct roots (which is to say Δ = 4A<sup>3</sup> + 27B<sup>2</sup> is nonzero). An additional point Ό at infinity is13 KB (2,172 words) - 17:46, 30 May 2021
- | [[Walther_MA271_Fall2020_topic17#3. Generating Fractals|3. Generating Fractals]] ...li. There are different types of self-similarity and many of them describe cases where the copies are not identical. <br />24 KB (3,663 words) - 01:01, 7 December 2020
- ...<math>j</math> do not communicate. The diagrams below illustrate these two cases. ...we can see that after transiting from state 1 to state 2, the state 2 and 3 become a closed set; namely, they are never going to return to state 1; the2 KB (390 words) - 02:57, 6 December 2020
- 3. When all events have no outcomes in common. 3. P(A∨B) = P(A) + P(B) - P(A∧B). When A and B are not mutually exclusive14 KB (2,441 words) - 16:10, 14 December 2022
- =&\begin{cases} \end{cases}26 KB (4,138 words) - 08:25, 6 December 2022
- ...example of an AI art model, but when we say model what do we mean? In most cases, especially in recent years, we are referring to a neural network or a comb ...1 neuron. Our input vector is <math> \begin{bmatrix} 0 \\ 0.1 \\ 0.2 \\ 0.3 \\ 0.4 \\ 0.5 \\ 0.6 \\ 0.7 \\ 0.8 \\ 0.9 \end{bmatrix} </math>. The weight15 KB (2,564 words) - 11:25, 29 November 2022
