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- By definition, we have that the variance of random variable <math>Z</math> is given by <br/>2 KB (333 words) - 14:17, 13 June 2013
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- ; within-class variance : <math>\sigma_W^2 = \omega_0 \sigma_0^2 + \omega_1 \sigma_1^2</math> ; between-class variance : <math>\sigma_B^2 = \omega_0 (\mu_0 - \mu_T)^2 + \omega_1 (\mu_1 - \mu_T)^14 KB (2,253 words) - 12:21, 9 January 2009
- * [[2008/10/02_MA375Fall2008walther]] - Recurrence Relations and sequences, variance and independence10 KB (1,377 words) - 14:49, 20 September 2012
- X(n) is i.i.d Gausian 0 mean with variance <math>\sigma_x^2</math><br/>3 KB (522 words) - 06:45, 16 September 2013
- You can follow the same rules for finding the mean and variance of y.2 KB (292 words) - 06:18, 2 April 2009
- '''Definition of expectation and variance''' and their properties3 KB (525 words) - 13:04, 22 November 2011
- ...r of candy bars you eat before you have all coupons. What are the mean and variance of <math>X</math>? [[5.1 - Chris Cadwallader_ECE302Fall2008sanghavi]] Variance4 KB (656 words) - 12:56, 22 November 2011
- Also, note for geom(p), variance is <math>\frac{1-p}{p^2}</math>. I don't think we can simply add all the v715 B (131 words) - 19:25, 6 October 2008
- This is my little scratchpad for the variance.231 B (48 words) - 10:13, 7 October 2008
- ==Variance==413 B (51 words) - 11:28, 7 October 2008
- ...ndently, with each one being a Gaussian random variable with zero mean and variance of 1. Let <math>D</math> be the square of the (random) distance of the poin3 KB (449 words) - 12:57, 22 November 2011
- ...ys that we need to generate a Gaussian variable, do we assume a mean and a variance?138 B (29 words) - 16:43, 20 October 2008
- == Problem 2: Bounded Variance == *(a) What is the maximum variance possible for a Bernoulli random variable?3 KB (528 words) - 12:58, 22 November 2011
- The problem only asks for the variance of a uniform R.V. on the interval [a,b] Thus using the formula for variance:325 B (62 words) - 13:17, 2 November 2008
- To find the maximum variance of a Bernoulli RV first find the variance equation. ...ual to 0 and find the value of p that results in the largest value for the variance.384 B (69 words) - 13:16, 2 November 2008
- the variance of a binomial random variable:490 B (94 words) - 07:00, 3 November 2008
- After maximizing the variance equation, we get the result as:150 B (26 words) - 18:56, 3 November 2008
- To ensure that the calculated maximum variance is indeed a maximum, and not a minimum, you must take the second derivative306 B (56 words) - 19:53, 3 November 2008
- ...math>f_Y(y)</math> of the random variable <math>Y</math>, and its mean and variance, <math>E[Y]</math>, and <math>Var[Y]</math>. ...h>0 < \alpha < 1/2</math>. Then find the conditional mean and conditional variance of <math>Y</math> given that <math>X = \alpha</math>.4 KB (703 words) - 12:58, 22 November 2011
- ...Both of your variances are wrong, remember that you can't have a negative variance. Use the Var[X] = E[X^2] - (E[X])^2 formula. (Gregory Pajot)1 KB (228 words) - 19:34, 9 December 2008
- a)Does any one know what to do to the variance when multiplied by a number? I know that when added together:408 B (78 words) - 11:10, 8 December 2008
- \\how do you find the variance? -carlos leon-195 B (27 words) - 17:51, 9 December 2008
- ...ormula, and from THAT, the variance should also be the same (also from the variance formula).560 B (111 words) - 11:50, 9 December 2008
- a)Does any one know what to do to the variance when multiplied by a number? I know that when added together:408 B (78 words) - 14:12, 9 December 2008
- *Please correct the posterior variance on page 19 (middle of the page): Assignment for "a" after the line "More sp3 KB (543 words) - 12:55, 12 December 2008
- Given this system and the definition of time variance2 KB (379 words) - 07:00, 10 September 2008
- = Time Invariance? or Time Variance? =1 KB (185 words) - 19:56, 10 September 2008
- == Linearity and Time Variance ==753 B (131 words) - 16:23, 11 September 2008
- == Time Variance ==331 B (57 words) - 13:02, 12 September 2008
- == Time Variance check ==616 B (112 words) - 11:11, 12 September 2008
- An example of time variance is turning on your T.V. to a channel. If you turn it on at 10:01 AM, the f549 B (107 words) - 14:25, 12 September 2008
- ...y Fisher's criterion, which applies exactly to Gaussian classes with equal variance and approximately to other models. Variants like Flexible discriminant anal ...zes the distance between the means of the two classes while minimizing the variance within each class. See Lecture 10 for detailed explanation.31 KB (4,832 words) - 18:13, 22 October 2010
- ...rix with random entries, chosen from a normal distribution with mean zero, variance one and standard deviation one. ...d we assume for the parameters of the distribution of mean? What about the variance?10 KB (1,594 words) - 11:41, 24 March 2008
- The univariate case. The variance is assumed to be known. ...be interpreted as: in making prediction for a single new observation, the variance of the estimate will have two components:10 KB (1,488 words) - 10:16, 20 May 2013
- This function has zero mean, H variance, an n-dimensional density, and is not compactly supported.10 KB (1,607 words) - 08:38, 17 January 2013
- ...in and test the system. We generated N = 10<sup>5</sup> samples. Also, the variance for each feature was the same and the mean of each class feature changed de4 KB (735 words) - 22:49, 8 March 2008
- ...zes the distance between the means of the two classes while minimizing the variance within each class.3 KB (430 words) - 10:40, 24 April 2008
- ...flect the correlation between the axis. The diagonal entries represent the variance along that direction(dimension) itself while the non diagonal entries repre3 KB (528 words) - 08:48, 10 April 2008
- The CRLB is the minimum variance achievable by any unbiased estimator for a parameter. ...mator that is unbiased and achieves the CRLB is referred to as the Minimum Variance Unbiased Estimator(MVUE).6 KB (995 words) - 10:39, 20 May 2013
- ...s which result tend to be fficient in the sense of having low within class variance. Applications are suggested for the problems of non-linear prediction, effi39 KB (5,715 words) - 10:52, 25 April 2008
- 4) Estimate of variance and other parameters is often biased ...certain specially-designed priors, leads naturally to unbiased estimate of variance2 KB (287 words) - 10:39, 20 May 2013
- ...h is the average value of the feature vectors. The second parameter is the variance which measures how much the data is scattered around the mean. If the mean of a normal distribution is zero and the variance is one then it is called standard normal distribution.2 KB (247 words) - 08:32, 10 April 2008
- ...that the autocorrelation function evaluated at the origin is equal to the variance of the sequence. I hope this helps. Good luck.2 KB (258 words) - 00:51, 22 March 2008
- ...zes the distance between the means of the two classes while minimizing the variance within each class. See [[Lecture 10_Old Kiwi]] for detailed explanation.3 KB (475 words) - 18:05, 28 March 2008
- ...y Fisher's criterion, which applies exactly to Gaussian classes with equal variance and approximately to other models. Variants like Flexible discriminant anal418 B (56 words) - 11:23, 25 March 2008
- (This is equal only if variance = 0)5 KB (1,003 words) - 08:40, 17 January 2013
- i.e. small variance in the training data can yield large variations in decision rules obtained.6 KB (806 words) - 08:42, 17 January 2013
- ...ts of a data set. The principal components are random variables of maximal variance constructed from linear combinations of the input features. Equivalently, t657 B (104 words) - 01:45, 17 April 2008
- which is the same as maximizing the between-cluster variance<center><math> S_{Total}=S_{W}+S_{B}</math></center> <center><math> tr(S_ ...the between-class variance is equivalent to minimizing the within-class variance.8 KB (1,244 words) - 08:44, 17 January 2013
- ...es from a spherical Normal distribution with different means but identical variance (and zero covariance). ...ks best for images with clusters that are spherical and that have the same variance.3 KB (528 words) - 14:33, 17 April 2008
- ...d embeds the data points in that subspace in a way that best preserves the variance of the input space (original high-dimensional space). If the input data poi4 KB (593 words) - 12:06, 18 April 2008
- ...hen the variances of two categories differ. In previous examples where the variance for both categories are the same, the Chernoff bound was close to the Bhatt17 KB (2,590 words) - 10:45, 22 January 2015
- ...oz-background-inline-policy: -moz-initial;" colspan="2" | Expectation and Variance of Random Variables3 KB (491 words) - 12:54, 3 March 2015
- ...o-able, since the abnomal sample is made far apart enough (compared to the variance of class1), but in the second example, it's just not possible to ditinguish5 KB (694 words) - 12:41, 2 February 2012
- ...nown. Finally, we looked at the slight "bias" problem when calculating the variance.833 B (115 words) - 09:15, 11 May 2010
- '''Example 2: 1D Gaussian with unknown mean and variance''' ...t{\Sigma}</math> over all data sets of size <math>N</math> is not the true variance <math>\Sigma</math>.7 KB (1,179 words) - 09:17, 11 May 2010
- <br/><br/>5. Expected value (used in ECE 438), variance (used in ECE 438) <br/><br/>6. Conditional/total pdf, pmf, expectation, variance2 KB (231 words) - 07:20, 4 May 2010
- ...distributed variables (i.i.d) with finite mean <math>\mu</math> and finite variance <math>\sigma^2>0</math>.Then as n increases the distribution of <math>\Sigm Xi has mean <math>\mu_i</math> and finite variance <math>\sigma^2 > 0</math> ,i=1,2,...,n5 KB (806 words) - 09:08, 11 May 2010
- ...y Fisher's criterion, which applies exactly to Gaussian classes with equal variance and approximately to other models. Variants like Flexible discriminant anal ...zes the distance between the means of the two classes while minimizing the variance within each class. See Lecture 10 for detailed explanation.31 KB (4,787 words) - 18:21, 22 October 2010
- ...nt, but that each have identical mean <math class="inline">\mu</math> and variance <math class="inline">\sigma^{2}</math> . Let <math class="inline">\mathbf{Y5 KB (928 words) - 17:46, 13 March 2015
- and <math>\mathbf{Y}</math> is a Gaussian random variable with mean 0 and variance 1. Let <math>\mathbf{U}</math> and <math>\mathbf{V}</math> be two new rando7 KB (1,103 words) - 05:27, 15 November 2010
- ...ath>\mathbf{X}</math> be a random variable with mean <math>\mu</math> and variance <math>\sigma^{2}</math>. Then <math>\forall\epsilon>0</math>3 KB (437 words) - 11:26, 16 November 2010
- What kind of pdf is the pdf you determined in part (b)? What is the mean and variance of a random variable with this pdf? ...}}^{2}}{\sigma_{\mathbf{X}}^{2}+\sigma_{\mathbf{N}}^{2}}\cdot y</math> and variance <math>\frac{\sigma_{\mathbf{X}}^{2}\sigma_{\mathbf{N}}^{2}}{\sigma_{\mathbf6 KB (939 words) - 04:20, 15 November 2010
- ='''1.4.4 Poisson distribution when mean and variance are <math class="inline">\lambda</math>'''=5 KB (921 words) - 11:25, 30 November 2010
- 1.8.2 Variance2 KB (305 words) - 11:15, 17 November 2010
- ...math> be a random variable with mean <math class="inline">\mu</math> and variance <math class="inline">\sigma^{2}</math> . Then <math class="inline">\forall\3 KB (435 words) - 11:38, 30 November 2010
- ...d.</math> random variables with mean <math class="inline">\mu</math> and variance <math class="inline">\sigma^{2}</math> . Define <math class="inline">\mathb You can show this is true as long as the mean exists. The variance need not exist. Proof for this is harder and not responsible for this.2 KB (303 words) - 11:39, 30 November 2010
- ...istributed random variables with mean <math class="inline">\mu</math> and variance <math class="inline">\sigma^{2}</math> , and <math class="inline">Cov\left(795 B (126 words) - 11:41, 30 November 2010
- ...''d''.</span> random vectors with mean <span class="texhtml">μ</span> and variance <span class="texhtml">σ<sup>2</sup></span> , such that <span class="texhtm ...le <math class="inline">\mathbf{Z}</math> that is Gaussian with mean 0 and variance 1 .4 KB (657 words) - 11:42, 30 November 2010
- ...{A}</math> has a mean <math class="inline">\mu_{\mathbf{A}}</math> and a variance <math class="inline">\sigma_{\mathbf{A}}^{2}</math> . Is <math class="inlin11 KB (1,964 words) - 11:52, 30 November 2010
- ...h class="inline">\mathbf{X}_{k}</math> are independent with zero mean and variance <math class="inline">\sigma_{k}^{2}</math> , then the sum exists in the MS5 KB (859 words) - 11:55, 30 November 2010
- ...<math class="inline">\mathbf{X}</math> be a random variable with mean 2 , variance 8 , and moment generating function <math class="inline">\phi_{\mathbf{X}}\l (b) Find the variance of <math class="inline">\mathbf{X}\left(t\right)</math> .22 KB (3,780 words) - 07:18, 1 December 2010
- (c) Find the variance of <math class="inline">\mathbf{M}</math> .12 KB (2,205 words) - 07:20, 1 December 2010
- Find the mean and variance of the output.6 KB (1,093 words) - 08:23, 27 June 2012
- ...nt, but that each have identical mean <math class="inline">\mu</math> and variance <math class="inline">\sigma^{2}</math> . Let <math class="inline">\mathbf{Y Find the mean and variance of <math class="inline">\mathbf{X}\left(t\right)</math> .10 KB (1,827 words) - 08:33, 27 June 2012
- ...thbf{X}</math> has mean <math class="inline">\mu_{\mathbf{X}}</math> and variance <math class="inline">\sigma_{\mathbf{X}}^{2}</math> . The correlation coeff ...mean <math class="inline">a\mu_{\mathbf{X}}+b\mu_{\mathbf{Y}}</math> and variance <math class="inline">a^{2}\sigma_{\mathbf{X}}^{2}+2rab\sigma_{\mathbf{X}}\s10 KB (1,652 words) - 08:32, 27 June 2012
- ...bf{M}=\frac{\mathbf{X}+\mathbf{Y}}{2}</math> is independent of the sample variance <math class="inline">\mathbf{V}=\left(\mathbf{X}-\mathbf{M}\right)^{2}+\lef If <math class="inline">\left|a\right|>1</math> , show that the variance of the process <math class="inline">\left\{ \mathbf{X}_{k}\right\}</math>6 KB (916 words) - 08:26, 27 June 2012
- ...{X}_{n}\right\}</math> , has mean <math class="inline">0</math> , and has variance <math class="inline">\sigma^{2}</math> . Define <math class="inline">\mathb10 KB (1,608 words) - 08:31, 27 June 2012
- Find the variance of <math class="inline">\mathbf{Z}</math> .9 KB (1,560 words) - 08:30, 27 June 2012
- ...th> be a sequence of independent, identically distributed zero-mean, unit-variance Gaussian random variables. The sequence <math class="inline">\mathbf{X}_{n} Find the mean and variance of <math class="inline">\mathbf{X}_{n}</math> .14 KB (2,439 words) - 08:29, 27 June 2012
- Find the mean and variance of <math class="inline">\mathbf{Y}_{n}</math> .12 KB (1,920 words) - 08:28, 27 June 2012
- What kind of pdf is the pdf you determined in part (b)? What is the mean and variance of a random variable with this pdf? ...}^{2}}{\sigma_{\mathbf{X}}^{2}+\sigma_{\mathbf{N}}^{2}}\cdot y</math> and variance <math class="inline">\frac{\sigma_{\mathbf{X}}^{2}\sigma_{\mathbf{N}}^{2}}{7 KB (1,015 words) - 11:59, 30 November 2010
- ...thbf{Y}</math> has mean <math class="inline">\mu_{\mathbf{Y}}</math> and variance <math class="inline">\sigma_{\mathbf{Y}}^{2}</math> , and that the correlat Find the variance of <math class="inline">\mathbf{Z}</math> .3 KB (504 words) - 12:00, 30 November 2010
- ..."inline">\mathbf{Y}</math> is a Gaussian random variable with mean 0 and variance 1 . Let <math class="inline">\mathbf{U}</math> and <math class="inline">\m5 KB (803 words) - 12:08, 30 November 2010
- ..."inline">\mathbf{Y}</math> is a Gaussian random variable with mean 0 and variance 1 . Let <math class="inline">\mathbf{U}</math> and <math class="inline">\m5 KB (803 words) - 12:10, 30 November 2010
- (c) Find the variance of <math class="inline">\mathbf{X}</math> .5 KB (793 words) - 12:10, 30 November 2010
- ...ed i.i.d. random variables with mean <math class="inline">\mu</math> and variance <math class="inline">\sigma^{2}</math> . Let <math class="inline">\mathbf{Y (a) Find the variance of <math class="inline">\mathbf{Y}_{M}</math> .2 KB (420 words) - 11:25, 16 July 2012
- | Variance6 KB (851 words) - 15:34, 23 April 2013
- *On expectation and/or variance of a discrete random variable7 KB (960 words) - 18:17, 23 February 2015
- ...ata. We define the two factors, redundancy and signal, with covariance and variance. ...e to correlate variance of the data with the strength of the signal- large variance means strong signal of data.6 KB (1,043 words) - 12:45, 3 March 2015
- ...in and test the system. We generated N = 10<sup>5</sup> samples. Also, the variance for each feature was the same and the mean of each class feature changed de5 KB (772 words) - 11:05, 10 June 2013
- This function has zero mean, H variance, an n-dimensional density, and is not compactly supported.10 KB (1,609 words) - 11:22, 10 June 2013
- The univariate case. The variance is assumed to be known. ...be interpreted as: in making prediction for a single new observation, the variance of the estimate will have two components:10 KB (1,472 words) - 11:16, 10 June 2013
- ...ve them perspective. The more varied my experiences became, so too did the variance in what I perceived as solutions increase. There is rarely one answer to a4 KB (666 words) - 12:13, 9 February 2012
- ...generating function of a Gaussian variable with mean <math>\mu</math> and variance <math>\sigma^2</math> where <br/>2 KB (453 words) - 14:19, 13 June 2013
- (This is equal only if variance = 0)6 KB (1,041 words) - 11:22, 10 June 2013
- i.e. small variance in the training data can yield large variations in decision rules obtained.6 KB (837 words) - 11:23, 10 June 2013
- .... More specifically, we discussed the fact that, under Gaussian noise, the variance of MLE asymptotically achieves the Cramer-Rao bound. We then warned that th2 KB (319 words) - 13:27, 8 March 2012
- The CRLB is the minimum variance achievable by any unbiased estimator for a parameter. ...mator that is unbiased and achieves the CRLB is referred to as the Minimum Variance Unbiased Estimator(MVUE).6 KB (976 words) - 13:25, 8 March 2012
- which is the same as maximizing the between-cluster variance<center><math> S_{Total}=S_{W}+S_{B}</math></center> <center><math> tr(S_ ...the between-class variance is equivalent to minimizing the within-class variance.8 KB (1,214 words) - 11:24, 10 June 2013
- ...nt, but that each have identical mean <math class="inline">\mu</math> and variance <math class="inline">\sigma^{2}</math> . Let <math class="inline">\mathbf{Y (b) Find the mean and variance of <math class="inline">\mathbf{X}\left(t\right)</math> .5 KB (780 words) - 01:25, 9 March 2015
- ...thbf{X}</math> has mean <math class="inline">\mu_{\mathbf{X}}</math> and variance <math class="inline">\sigma_{\mathbf{X}}^{2}</math> . The correlation coeff (c) Find the variance of <math class="inline">\mathbf{Z}</math> . Express your answer in terms of5 KB (766 words) - 00:16, 10 March 2015
- ...{X}_{n}\right\}</math> , has mean <math class="inline">0</math> , and has variance <math class="inline">\sigma^{2}</math> . Define <math class="inline">\mathb5 KB (729 words) - 00:51, 10 March 2015
- ...th> be a sequence of independent, identically distributed zero-mean, unit-variance Gaussian random variables. The sequence <math class="inline">\mathbf{X}_{n} Find the mean and variance of <math class="inline">\mathbf{X}_{n}</math> .5 KB (726 words) - 10:35, 10 March 2015
- Find the mean and variance of <math class="inline">\mathbf{Y}_{n}</math> .4 KB (632 words) - 11:05, 10 March 2015
- Find the mean and variance of the output.4 KB (616 words) - 10:19, 13 September 2013
- Find the variance of <math class="inline">\mathbf{Z}</math> .4 KB (572 words) - 10:24, 10 March 2015
- ...math> be a random variable with mean <math class="inline">\mu</math> and variance <math class="inline">\sigma^{2}</math> . Then <math class="inline">\forall\3 KB (532 words) - 10:36, 13 September 2013
- Find the mean and variance of the output.2 KB (234 words) - 10:37, 13 September 2013
- ...e } Y(t) \text{ is WSS, its mean is constant and does not depend on . For variance}6 KB (932 words) - 10:30, 13 September 2013
- ...s_point_3_ECE302_Spring2012_Boutin| Invent a problem on expectation and/or variance of a discrete random variable]] (0.5% course grade bonus)10 KB (1,422 words) - 20:14, 30 April 2013
- *2.3 Moments of discrete random variable (expectation, variance) *3.2 Moments of a continuous random variables (expectation, variance)4 KB (498 words) - 10:18, 17 April 2013
- ...ng the random variable by a constant "a" has the effect of multiplying the variance by <math>a^2</math>.2 KB (336 words) - 12:59, 18 February 2013
- ...t we had already seen that relation when we looked at the expectation and variance of aX+b in general.3 KB (393 words) - 08:21, 27 February 2013
- Invent a problem related to the expectation and/or variance of a discrete random variable and solve it. Then post your problem and solu [[Category:variance]]3 KB (467 words) - 18:17, 27 February 2013
- ...[[Category:discrete random variable]] [[Category:expectation]] [[Category:variance]] ...solve numerically.<br> b)What effect does increasing r to .99 have on the variance? Please note that round-off error can be somewhat significant when perform4 KB (757 words) - 06:59, 22 February 2013
- ...] [[Category:discrete random variable]][[Category:expectation]] [[Category:variance]] To find the variance value of Z We have to find values of E[Z^2] and E[Z].<br>2 KB (299 words) - 18:13, 27 February 2013
- In Lecture 30, we defined various 1D and 2D signals (mean, variance, autocorrelation, autocovariance) that can be used to describe the statisti2 KB (265 words) - 12:15, 25 March 2013
- and where the expected squared deviation or ''variance'' is ...a;)'' which says that ''x'' is distributed normally with mean ''μ'' and variance ''σ<sup>2</sup>''. Samples from normal distributions tend to cluster5 KB (844 words) - 05:43, 13 April 2013
- ...on of sum processes. In particular, we obtained simple expressions for the variance and autocovariance of a sum process. We also described two important proper2 KB (299 words) - 06:44, 12 April 2013
- ...that the autocorrelation function evaluated at the origin is equal to the variance of the sequence. I hope this helps. Good luck.2 KB (264 words) - 08:05, 9 April 2013
- ...n the features are statistically independent and each feature has the same variance, σ<sup>2</sup>. Here, the covariance matrix is diagonal since its sim ...squared distance ||'''x - μ'''||<sup>2</sup> must be normalized by the variance σ<sup>2</sup> and offset by adding ln ''P''(''w<sub>i</sub>''); there11 KB (1,792 words) - 16:09, 19 April 2013
- ...ou will obtain the definition of variance. Another popular way of defining variance is The standard deviation is simply the square root of the variance.7 KB (1,146 words) - 06:19, 5 May 2013
- ** [[2008/10/02_MA375Fall2008walther]] - Recurrence Relations and sequences, variance and independence1 KB (167 words) - 09:33, 20 May 2013
- ...ations_of_independent_gaussian_RVs|(proof)]] characterized by a mean and a variance.6 KB (1,084 words) - 13:20, 13 June 2013
- *[[variance_of_LC_of_RVs|Variance of a Linear Combination of Random Variables]]2 KB (227 words) - 11:15, 6 October 2013
- By definition, we have that the variance of random variable <math>Z</math> is given by <br/>2 KB (333 words) - 14:17, 13 June 2013
- ...andom variable that is Gaussian distributed with mean <math>\mu</math> and variance <math>\sigma^2</math>.]]</center>15 KB (2,637 words) - 12:11, 21 May 2014
- ...ote:''' <math>\qquad</math> E[(X - <math>\mu_X)^2</math>] is called the '''variance''' of X and is often denoted <math>\sigma_X</math><math>^2</math>. The posi Moments generalize mean and variance to nth order expectations.8 KB (1,474 words) - 12:12, 21 May 2014
- Let X be a random variable with mean <math>\mu</math> and variance <math>\sigma^2</math>. Then, <br/> ...math> be a sequence of iid random variables with mean <math>\mu</math> and variance <math>\sigma^2</math>. Let <br/>15 KB (2,578 words) - 12:13, 21 May 2014
- ...or random variable <math>\mathbf{X}</math> with mean <math>\mu</math> and variance <math>\sigma^2</math>. In constructing your proof, keep in mind that <math>3 KB (449 words) - 21:36, 5 August 2018
- ...te and prove the Chebyshev inequality for random variable with mean μ and variance σ<sup>2</sup>. In constructing your proof, keep in mind that may be either ...or discrete random variable with mean <span class="texhtml">μ</span> and variance <span class="texhtml">σ<sup>2</sup></span>. Then, <math>\forall \varepsilo6 KB (995 words) - 09:21, 15 August 2014
- ...erivation of PCA could be found in [4]). Following this idea of maximizing variance, let's derive the formula for PCA. ...mension <span class="texhtml">''P'' < ''M''</span> while maximizing the variance of the projected data. For now we will assume that <span class="texhtml">''22 KB (3,459 words) - 10:40, 22 January 2015
- ...s that the components of our new random variable are uncorrelated and have variance 1. This process is called whitening because the output resembles a white no ...ix. Finally, we must scale the different components so that they have unit variance. In order to do this, we need the eigendecomposition of the original covari17 KB (2,603 words) - 10:38, 22 January 2015
- *Maximum Likelihood Estimate is efficient: (the estimates have the smallest variance).25 KB (4,187 words) - 10:49, 22 January 2015
- ...ossible (signal representation), then the components that have the largest variance in feature values within classes are kept, which is known as [[PCA|''Princi9 KB (1,419 words) - 10:41, 22 January 2015
- In order to form a Gaussian distribution, the variance <math>\sigma_n^2</math> associated with <math>\mu_n</math> could also be ob8 KB (1,268 words) - 08:31, 29 April 2014
- ...le of using maximum likelihood estimation (MLE) to estimation the mean and variance of Gaussian data. Finally an experiment was performed to show Bayes classif2 KB (259 words) - 12:40, 2 May 2014
- ...to choose the project axes are very important tasks. PCA uses the largest variance axes as a projection axes whereas LDA decides these axes based on the best4 KB (628 words) - 09:44, 30 April 2014
- ...> and <math>\hat{\sigma{}^{2}}</math> are the estimated Mean and estimated Variance.12 KB (1,986 words) - 10:49, 22 January 2015
- ...leq 2P^*</math>). Obviously we can get better error bound by observing the variance where14 KB (2,313 words) - 10:55, 22 January 2015
- == Convergence of the mean and variance == ...x}_n</math>, <math>p_n</math> has mean <math>E(p_n(\textbf{x}))</math> and variance <math>Var(p_n(\textbf{x}))</math>. Thus, <math>p_n(\textbf{x})</math> conve11 KB (1,824 words) - 10:53, 22 January 2015
- ...density estimation. The report also covers the convergence of the mean and variance as sample size grows to the infinity. In last part, it explains about relat2 KB (333 words) - 09:32, 1 May 2014
- ...istributed, and use maximum likelihood estimation to estimate the mean and variance of the training data. Then calculate the Bayesian probability and make the **Parameter estimation for mean,variance9 KB (1,382 words) - 10:47, 22 January 2015
- Similarly, the variance of the estimator is given by Since the bias, variance, and the MSE of the estimator will depend on the specific value of <math>\t14 KB (2,356 words) - 20:48, 30 April 2014
- ...an Form and the two most decisive parameters in Gaussian R.V. are mean and variance) Please note that <math>\bar{x_n}</math> is the empirical mean in our known Given the posteriori density <math>p(\mu|D)</math> successfully derived (variance: <math>\sigma_n^2</math> and mean: <math>\mu_n</math> now known), the final10 KB (1,625 words) - 10:51, 22 January 2015
- ...arphi(\vec{X})</math> is a density function and the values of the mean and variance of the estimated p.d.f. converge. That is, <math>p_n(\vec{X})\xrightarrow{n16 KB (2,703 words) - 10:54, 22 January 2015
- Often, a real-world data contains either high variance or high bias hence it is difficult to estimate true density and using such ...isson, its distribution is approximately normal with mean of $\lambda$ and variance of $\lambda$ by the central limit theorem.16 KB (2,400 words) - 23:34, 29 April 2014
- ...each case, we account 30 trials, which will give us a reasonable mean and variance, where the ground truth of p is 2/3. <center>[[Image:ywfig5.png|600px|Figure 2:Variance of <math>\hat{p}</math> with different prior information]] </center>10 KB (1,600 words) - 10:52, 22 January 2015
- ...rate a good quality of data. Often, a real-world data contains either high variance or high bias hence it is difficult to estimate true density and using such ...distribution is approximately normal with mean of <math>\lambda</math> and variance of <math>\lambda</math> by the central limit theorem. As a result, a normal18 KB (2,852 words) - 10:40, 22 January 2015
- Similarly, the variance of the estimator is given by Since the bias, variance, and the MSE of the estimator will depend on the specific value of <math>\t19 KB (3,418 words) - 10:50, 22 January 2015
- ...d estimate the entire distribution by finding the parameters (the mean and variance for the gaussian example) of that distribution.9 KB (1,604 words) - 10:54, 22 January 2015
- ...is perfectly unbiased already. Increasing k has the effect of reducing the variance of the estimate of <math>\rho(\vec{x_o}) </math>, but the expectation of <m ...he KNN method does not improve in average accuracy as k increases, but the variance of the accuracy does decrease with increasing k. An advantage of the neares6 KB (1,013 words) - 10:55, 22 January 2015
- - Details about the 1D example are missing. For example, what is the mean and variance of the distributions shown in the figure? How many training data and testin1 KB (241 words) - 14:01, 6 May 2014
- ...leq 2P^*</math>). Obviously we can get better error bound by observing the variance where14 KB (2,323 words) - 04:54, 1 May 2014
- ...leq 2P^*</math>). Obviously we can get better error bound by observing the variance where14 KB (2,340 words) - 17:24, 12 May 2014
- *Bias: The maximum likelihood for the variance $\sigma^2$ is biased means ...er all data sets of size n of the sample variance is not equal to the true variance:11 KB (2,046 words) - 10:51, 22 January 2015
- 'Bias: The maximum likelihood for the variance $\sigma^2$ is biased means.', $\sigma^2$ was not transformed to Wiki format2 KB (291 words) - 17:01, 12 May 2014
- ...sic idea of the frequentist estimation, how to calculate the bias and variance of the estimator, and some properties of estimators for evaluation purpose. ...be more concise if example 1 and 2 can be combined since knowledge of variance doesn't affect the estimation of the mean. Following this, the bias of both2 KB (320 words) - 10:20, 6 May 2014
- ...n> is called the scatter of the data, and is similar to the idea of sample variance. Intuitively, this cost function is maximized when the projected means are10 KB (1,684 words) - 13:00, 5 May 2014
- ...n> is called the scatter of the data, and is similar to the idea of sample variance. Intuitively, this cost function is maximized when the projected means are10 KB (1,666 words) - 10:56, 22 January 2015
- ...math>, so that <math>f_X(x)=\lambda{exp}(-\lambda{x})u(x)</math>. Find the variance of <math>X</math>. You must show all of your work.3 KB (470 words) - 07:47, 4 November 2014
- Find the mean and variance of <math>S_n = X_1 + ...+ X_n</math>5 KB (927 words) - 16:43, 24 February 2017
- ...math>, so that <math>f_X(x)=\lambda{exp}(-\lambda{x})u(x)</math>. Find the variance of <math>X</math>. You must show all of your work.3 KB (534 words) - 21:02, 5 August 2018
- (b) Find the mean and variance of <math class="inline">\mathbf{X}\left(t\right)</math> .4 KB (700 words) - 17:48, 13 March 2015
- ...thbf{X}</math> has mean <math class="inline">\mu_{\mathbf{X}}</math> and variance <math class="inline">\sigma_{\mathbf{X}}^{2}</math> . The correlation coeff ...mean <math class="inline">a\mu_{\mathbf{X}}+b\mu_{\mathbf{Y}}</math> and variance <math class="inline">a^{2}\sigma_{\mathbf{X}}^{2}+2rab\sigma_{\mathbf{X}}\s3 KB (525 words) - 00:20, 10 March 2015
- ...bf{M}=\frac{\mathbf{X}+\mathbf{Y}}{2}</math> is independent of the sample variance <math class="inline">\mathbf{V}=\left(\mathbf{X}-\mathbf{M}\right)^{2}+\lef If <math class="inline">\left|a\right|>1</math> , show that the variance of the process <math class="inline">\left\{ \mathbf{X}_{k}\right\}</math>6 KB (895 words) - 00:41, 10 March 2015
- ...{X}_{n}\right\}</math> , has mean <math class="inline">0</math> , and has variance <math class="inline">\sigma^{2}</math> . Define <math class="inline">\mathb3 KB (538 words) - 00:54, 10 March 2015
- Find the variance of <math class="inline">\mathbf{Z}</math> .4 KB (571 words) - 10:24, 10 March 2015
- ...th> be a sequence of independent, identically distributed zero-mean, unit-variance Gaussian random variables. The sequence <math class="inline">\mathbf{X}_{n} Find the mean and variance of <math class="inline">\mathbf{X}_{n}</math> .4 KB (692 words) - 10:36, 10 March 2015
- ...be a normal random variable with mean <math class="inline">\mu</math> and variance 1 . We want to find <math class="inline">E\left[\Phi\left(\mathbf{X}\right)3 KB (490 words) - 10:36, 10 March 2015
- Find the mean and variance of <math class="inline">\mathbf{Y}_{n}</math> .4 KB (699 words) - 11:08, 10 March 2015
- ...stic function of a Gaussian random variable with mean <math>\mu</math> and variance <math>\sigma^2</math> is <math>(e^{i\omega\mu-\frac{1}{2}\sigma^2\omega^2}) ...> is a Gaussian random variable with mean <math>(\eta_X+\eta_Y)</math> and variance <math>(\sigma_X^2+2\sigma_X\sigma_Yr+\sigma_Y^2)</math>5 KB (882 words) - 01:54, 31 March 2015
- <math>\mathbf{X}</math> is a Gaussian process with variance <math>\sigma^2=1</math>, <math>\mu_x=0</math>. From proof, we know if <math8 KB (1,336 words) - 01:53, 31 March 2015
- %% var decides the variance of the filter2 KB (316 words) - 00:15, 30 November 2015
- %% var decides the variance of the filter2 KB (316 words) - 00:25, 30 November 2015
- b) Calculate the variance of <math> Y_x</math>, i.e. <math>E[(Y_x-E[Y_x])^2]</math>.3 KB (524 words) - 12:53, 7 December 2015
- ...X_n</math>, where each <math>X_i</math> has mean <math>\mu = 0</math> and variance <math> \sigma^2</math>. Show that for every <math>i=1,...,n</math> the rand2 KB (351 words) - 00:17, 4 December 2015
- ...ummation effects from the multiple sources can lead to significant spatial variance in the frequency response. If two audio sources are at a similar level and2 KB (298 words) - 00:06, 24 April 2017
- ...th> x(m,n)</math>, are i.i.d. Gaussian random variables with mean zero and variance one. Calculate the auto covariance given by3 KB (566 words) - 16:39, 18 May 2017
- ...r ranges resulting in less variance and larger ranges resulting in greater variance.7 KB (1,183 words) - 00:53, 3 December 2018
- ...al district size, and a normal distribution around the mean district size. Variance was mentioned again by the majority as a traditional method of proper repre ...better methods available, but believed that Huntington-Hill minimized the variance from true size, and did not think there was enough evidence to overturn the3 KB (410 words) - 00:11, 3 December 2018
- In conclusion, there is some variance when comparing english vowel pronunciations to more well-known frequencies,12 KB (1,785 words) - 10:53, 28 November 2019
- ...one. The matrix shown below is a Gaussian filter with the size of 5*5 and variance 1:4 KB (624 words) - 09:11, 6 December 2019
- ...ng the vertical axis while the horizontal axis has a significant amount of variance. Because of this fact, we can flatten the vertical dimension without losing8 KB (1,200 words) - 14:07, 5 December 2020
- ...e are. Usually denoted by σ. The standard deviation is the square root of variance. ...re of the standard deviation. It is used in calculation more often because variance is much easier to manipulate without the loss of data. It is also used beca2 KB (358 words) - 22:58, 6 December 2020
- ...e parameter θ, or Fischer information <math>I(θ)</math>, is equal to the variance of the score.<br />2 KB (261 words) - 22:03, 6 December 2020
- Variance can also be shown as differences between the expected value of the square o Using the identity of variance above, we can show that: <br />2 KB (351 words) - 23:13, 6 December 2020
- ...0is%20a%20statistic,data%20closer%20to%20the%20mean| Standard Deviation vs Variance]<br />847 B (112 words) - 23:12, 6 December 2020
- “Standard Deviation versus Variance.” Standard Deviation and Variance, www.mathsisfun.com/data/standard-deviation.html <br /> ...edia.com/ask/answers/021215/what-difference-between-standard-deviation-and-variance.asp#:~:text=Standard deviation is a statistic,data closer to the mean.<br /2 KB (184 words) - 23:38, 6 December 2020
