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- =Addition of two independent Poisson random variables = ...athbf{X}</math> and <math>\mathbf{Y}</math> are independent Poisson random variables with means <math>\lambda</math> and <math>\mu</math>, respectively.3 KB (557 words) - 11:11, 25 September 2013
- == Example. Addition of two independent Gaussian random variables == ...is the pdf you determined in part (b)? What is the mean and variance of a random variable with this pdf?6 KB (939 words) - 03:20, 15 November 2010
- == Example. Addition of multiple independent Exponential random variables == ...h parameter <math>\lambda</math> and <math>\mathbf{N}</math> is Geometric random variable with parameter <math>p</math>. Find the distribution of <math>\mat2 KB (268 words) - 03:18, 15 November 2010
- =Example. Addition of two independent Poisson random variables= ...and <math class="inline">\mathbf{Y}</math> are independent Poisson random variables with means <math class="inline">\lambda</math> and <math class="inline">\m3 KB (532 words) - 10:58, 30 November 2010
- =Example. Addition of two independent Gaussian random variables= ...is the pdf you determined in part (b)? What is the mean and variance of a random variable with this pdf?7 KB (1,015 words) - 10:59, 30 November 2010
- =Example. Two jointly distributed independent random variables= ..."inline">\mathbf{Y}</math> be two jointly distributed, independent random variables. The pdf of <math class="inline">\mathbf{X}</math> is5 KB (803 words) - 11:08, 30 November 2010
- [[ECE600_F13_notes_mhossain|'''The Comer Lectures on Random Variables and Signals''']] <font size= 3> Topic 12: Independent Random Variables</font size>2 KB (449 words) - 11:12, 21 May 2014
Page text matches
- A & B are independent if <math>P(A\cap B)=P(A)P(B)</math> side note: if A&B are independent then P(A|B)=P(A)3 KB (525 words) - 12:04, 22 November 2011
- == Problem 1: Arbitrary Random Variables == Let <math>U</math> be a uniform random variable on [0,1].4 KB (596 words) - 11:57, 22 November 2011
- *The sum of many, small independent things For 2 independent Gaussians:4 KB (722 words) - 12:05, 22 November 2011
- The PDF of the sum of two independent random variables is the convolution of the two PDFs. The lecture notes from 10/10 are helpf133 B (23 words) - 18:13, 19 October 2008
- == Problem 1: Random Point, Revisited== In the following problems, the random point (X , Y) is uniformly distributed on the shaded region shown.4 KB (703 words) - 11:58, 22 November 2011
- ...observed should be the sum or mean of many independent random variables. (variables need not be iid)(See the PROOF ) undirected graphs (Markov random fields), probabilistic decision trees/models have a number of31 KB (4,832 words) - 17:13, 22 October 2010
- ...ormally distributed random numbers : ex) RANDN(N) is an N-by-N matrix with random entries, chosen from a normal distribution with mean zero, variance one and ...ro generate a vecort of n-gaussian random variables ? can this be called a random vector ? BAsically my question is how do we simulate gaussian data whcih h10 KB (1,594 words) - 10:41, 24 March 2008
- which datasets with tens or hundreds of thousands of variables are available. These areas include ...tion of the nearest of a set of previously classified points. This rule is independent of the underlying joint distribution on the sample points and their classif39 KB (5,715 words) - 09:52, 25 April 2008
- ...ion case, there will be very large set of feature vectors and classes, and independent of the probability distributions of features, the sum of the distributions The following histograms of N uniformly distributed random variables for different values of N can be given to visualize the [http://en.wikipedi2 KB (247 words) - 07:32, 10 April 2008
- ...iable" being observed should be the sum or mean of many independent random variables.213 B (35 words) - 09:01, 31 March 2008
- | align="right" style="padding-right: 1em;" | The intersection of two independent events A and B ...e-policy: -moz-initial;" colspan="2" | Expectation and Variance of Random Variables3 KB (491 words) - 11:54, 3 March 2015
- let X1,X2,...,Xn be n independent and identically distributed variables (i.i.d) with finite mean <math>\mu</math> and finite variance <math>\sigma^ More precisely the random variable <math>Z_n = \frac{\Sigma_{i=1}^n X_i - n \mu}{\sigma \sqrt{n}}</ma5 KB (806 words) - 08:08, 11 May 2010
- ...I reduced it to [1 2 3; 0 -3 -3]. I'm not even sure whether plugging in random values was the right idea, but I'm stuck here. How do I proceed from here? ...That's like doing an experiment in science. You'd have to plug in lots of random values if you were doing science, but you'd miss the key points in math. Y4 KB (756 words) - 03:25, 8 September 2010
- ...observed should be the sum or mean of many independent random variables. (variables need not be iid)(See the PROOF ) undirected graphs (Markov random fields), probabilistic decision trees/models have a number of31 KB (4,787 words) - 17:21, 22 October 2010
- = [[ECE]] 600: Random Variables and Stochastic Processes = :*[[ECE 600 Sequences of Random Variables|2. Sequences of Random Variables]]2 KB (238 words) - 11:14, 25 September 2013
- [[Category:random variables]] Question 1: Probability and Random Processes1 KB (191 words) - 16:42, 13 March 2015
- [[Category:random variables]] Question 1: Probability and Random Processes5 KB (928 words) - 16:46, 13 March 2015
- =Addition of two independent Poisson random variables = ...athbf{X}</math> and <math>\mathbf{Y}</math> are independent Poisson random variables with means <math>\lambda</math> and <math>\mu</math>, respectively.3 KB (557 words) - 11:11, 25 September 2013
- == Example. Two jointly distributed random variables == Two joinly distributed random variables <math>\mathbf{X}</math> and <math>\mathbf{Y}</math> have joint pdf7 KB (1,103 words) - 04:27, 15 November 2010
- == Example. Addition of two independent Gaussian random variables == ...is the pdf you determined in part (b)? What is the mean and variance of a random variable with this pdf?6 KB (939 words) - 03:20, 15 November 2010
- == Example. Addition of multiple independent Exponential random variables == ...h parameter <math>\lambda</math> and <math>\mathbf{N}</math> is Geometric random variable with parameter <math>p</math>. Find the distribution of <math>\mat2 KB (268 words) - 03:18, 15 November 2010
- Two independent Poisson process <math class="inline">\mathbf{N}_{1}\left(t\right)</math> a ...th class="inline">PP\left(\lambda_{i}\right),\; i=1,2,\cdots,n</math> and independent each other. If <math class="inline">\mathbf{N}\left(t\right)=\sum_{i=1}^{n}5 KB (920 words) - 10:26, 30 November 2010
- ='''1.10 Two Random Variables'''= ...bf{Y}</math> be two jointly-distributed, statistically independent random variables, having pdfs <math class="inline">f_{\mathbf{X}}\left(x\right)</math> and6 KB (952 words) - 10:31, 30 November 2010
- =2.6 Random Sum= Example. Addition of multiple independent Exponential random variables2 KB (310 words) - 10:44, 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
- ...cdots</math> be a sequence of independent, identically distributed random variables, each having pdf ...ht)}\left(x\right).</math> Let <math class="inline">Y_{n}</math> be a new random variable defined by10 KB (1,713 words) - 06:17, 1 December 2010
- ...class="inline">\mathbf{X}\left(t,\omega\right)</math> , then we have a new random process <math class="inline">\mathbf{Y}\left(t\right)</math> : <math class= We will assume that <math class="inline">T</math> is deterministic (NOT random). Think of <math class="inline">\mathbf{X}\left(t\right)=\text{input to a s11 KB (1,964 words) - 10:52, 30 November 2010
- [[Category:random variables]] We place at random n points in the interval <math class="inline">\left(0,1\right)</math> and5 KB (859 words) - 10:55, 30 November 2010
- ...endent Poisson random variables|Addition of two independent Poisson random variables]] ...dent Gaussian random variables|Addition of two independent Gaussian random variables]]1 KB (188 words) - 10:57, 30 November 2010
- ...1 dime. One of the boxes is selected at random, and a coin is selected at random from that box. The coin selected is a quater. What is the probability that – A = Box selected at random contains at least one dime.22 KB (3,780 words) - 06:18, 1 December 2010
- ...Are <math class="inline">A</math> and <math class="inline">B^{C}</math> independent? (You must prove your result). <math class="inline">\therefore A\text{ and }B^{C}\text{ are independent. }</math>6 KB (1,093 words) - 07:23, 27 June 2012
- Consider the following random experiment: A fair coin is repeatedly tossed until the same outcome (H or T ...math> , respectively. Let <math class="inline">\mathbf{Z}</math> be a new random variable defined as <math class="inline">\mathbf{Z}=\mathbf{X}+\mathbf{Y}.<10 KB (1,827 words) - 07:33, 27 June 2012
- ...ft(x\right)=P\left(\left\{ \mathbf{X}\leq x\right\} \right)</math> of the random variable <math class="inline">\mathbf{X}</math> . Make sure and specify you ...inline">\mathbf{Y}</math> is <math class="inline">r</math> . Define a new random variable <math class="inline">\mathbf{Z}</math> by <math class="inline">\m10 KB (1,652 words) - 07:32, 27 June 2012
- ...inline">\mathbf{Y}</math> be jointly Gaussian (normal) distributed random variables with mean <math class="inline">0</math> , <math class="inline">E\left[\math ...stributed r.v's with identical means and variances but are not necessarily independent. Show that the r.v. <math class="inline">\mathbf{V}=\mathbf{X}+\mathbf{Y}</6 KB (916 words) - 07:26, 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 assigning10 KB (1,608 words) - 07:31, 27 June 2012
- ...f{Y}</math> be two independent identically distributed exponential random variables having mean <math class="inline">\mu</math> . Let <math class="inline">\mat ...that it deals with the exponential random variable rather than the Poisson random variable.14 KB (2,358 words) - 07:31, 27 June 2012
- Assume that <math class="inline">\mathbf{X}</math> is a binomial distributed random variable with probability mass function (pmf) given by <math class="inline" ...athbf{X}_{n},\cdots</math> be a sequence of binomially distributed random variables, with <math class="inline">\mathbf{X}_{n}</math> having probability mass f10 KB (1,754 words) - 07:30, 27 June 2012
- ...d <math class="inline">\mathbf{Y}</math> be two joinly distributed random variables having joint pdf ...athbf{X}</math> and <math class="inline">\mathbf{Y}</math> statistically independent? Justify your answer.9 KB (1,560 words) - 07:30, 27 June 2012
- ...ependent, identically distributed zero-mean, unit-variance Gaussian random variables. The sequence <math class="inline">\mathbf{X}_{n}</math> , <math class="inl ...ath class="inline">\mathbf{X}_{n}</math> is a sequence of Gaussian random variables with zero mean and variance <math class="inline">\sigma_{\mathbf{X}_{n}}^{214 KB (2,439 words) - 07:29, 27 June 2012
- ...line">\mathbf{Y}</math> be two independent identically distributed random variables taking on values in <math class="inline">\mathbf{N}</math> (the natural nu ...y distributed random variables, with the <math class="inline">n</math> -th random variable <math class="inline">\mathbf{X}_{n}</math> having pmf <math class10 KB (1,636 words) - 07:29, 27 June 2012
- =Example. Addition of two independent Poisson random variables= ...and <math class="inline">\mathbf{Y}</math> are independent Poisson random variables with means <math class="inline">\lambda</math> and <math class="inline">\m3 KB (532 words) - 10:58, 30 November 2010
- =Example. Addition of two independent Gaussian random variables= ...is the pdf you determined in part (b)? What is the mean and variance of a random variable with this pdf?7 KB (1,015 words) - 10:59, 30 November 2010
- =Example. Two jointly distributed independent random variables= ..."inline">\mathbf{Y}</math> be two jointly distributed, independent random variables. The pdf of <math class="inline">\mathbf{X}</math> is5 KB (803 words) - 11:08, 30 November 2010
- =Example. Two jointly distributed independent random variables= ..."inline">\mathbf{Y}</math> be two jointly distributed, independent random variables. The pdf of <math class="inline">\mathbf{X}</math> is5 KB (803 words) - 11:10, 30 November 2010
- =Example. Mean of i.i.d. random variables= ...ath> be <math class="inline">M</math> jointly distributed i.i.d. random variables with mean <math class="inline">\mu</math> and variance <math class="inline2 KB (420 words) - 10:25, 16 July 2012
- =Example. A sum of a random number of i.i.d. Gaussians= ...{ \mathbf{X}_{n}\right\}</math> be a sequence of i.i.d. Gaussian random variables, each having characteristic function2 KB (426 words) - 06:15, 1 December 2010
- *Discrete Random Variables ...on_ECE302S13Boutin|Normalizing the probability mass function of a discrete random variable]]7 KB (960 words) - 17:17, 23 February 2015
- The linear combination of independent Gaussian random variables is also Gaussian. ...</math> are <math>n</math> independent Gaussian random variables, then the random variable <math>Y</math> is also Gaussian, where <math>Y</math> is a linear2 KB (453 words) - 13:19, 13 June 2013
- ...h>M_{Xi}(t)</math>, <math>i = 1,2,...,n</math>, and if <math>Y</math> is a random variable resulting from a linear combination of <math>X_i</math>s such that ...s can be written as the product of the expectations of functions of random variables (proof). <br/>1 KB (261 words) - 13:17, 13 June 2013
- [[Category:random variables]] Question 1: Probability and Random Processes5 KB (763 words) - 09:57, 10 March 2015
