Create the page "Independent random variables" on this wiki! See also the search results found.
- == 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) - 04:18, 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) - 11:26, 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) - 11:31, 30 November 2010
- =2.6 Random Sum= Example. Addition of multiple independent Exponential random variables2 KB (310 words) - 11:44, 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) - 11:47, 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) - 07:17, 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) - 11:52, 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) - 11:55, 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) - 11:57, 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) - 07:18, 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) - 08:23, 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) - 08:33, 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) - 08:32, 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) - 08:26, 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) - 08:31, 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) - 08:31, 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) - 08:30, 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) - 08:30, 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) - 08:29, 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) - 08:29, 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) - 11:58, 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) - 11:59, 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) - 12:08, 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) - 12:10, 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) - 11:25, 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) - 07:15, 1 December 2010
- *Discrete Random Variables ...on_ECE302S13Boutin|Normalizing the probability mass function of a discrete random variable]]7 KB (960 words) - 18:17, 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) - 14:19, 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) - 14:17, 13 June 2013
- [[Category:random variables]] Question 1: Probability and Random Processes5 KB (763 words) - 10:57, 10 March 2015
- [[Category:random variables]] Question 1: Probability and Random Processes5 KB (780 words) - 01:25, 9 March 2015
- [[Category:random variables]] Question 1: Probability and Random Processes5 KB (766 words) - 00:16, 10 March 2015
- [[Category:random variables]] Question 1: Probability and Random Processes5 KB (729 words) - 00:51, 10 March 2015
- [[Category:random variables]] Question 1: Probability and Random Processes5 KB (735 words) - 01:17, 10 March 2015
- [[Category:random variables]] Question 1: Probability and Random Processes4 KB (609 words) - 01:54, 10 March 2015
- [[Category:random variables]] Question 1: Probability and Random Processes5 KB (726 words) - 10:35, 10 March 2015
- [[Category:random variables]] Question 1: Probability and Random Processes4 KB (616 words) - 10:19, 13 September 2013
- [[Category:random variables]] Question 1: Probability and Random Processes4 KB (572 words) - 10:24, 10 March 2015
- [[Category:random variables]] Question 1: Probability and Random Processes5 KB (748 words) - 01:01, 10 March 2015
- [[Category:random variables]] Question 1: Probability and Random Processes4 KB (655 words) - 10:36, 13 September 2013
- [[Category:random variables]] Question 1: Probability and Random Processes4 KB (547 words) - 16:40, 30 March 2015
- Probability, Statistics, and Random Processes for Electrical Engineering, 3rd Edition, by Alberto Leon-Garcia, *Discrete Random Variables10 KB (1,422 words) - 20:14, 30 April 2013
- ...n Part III of the material with a definition of the concept of "continuous random variable" along with two examples.2 KB (321 words) - 11:12, 15 February 2013
- ...discrete) and we began discussing normally distributed (continuous) random variables. ...on_ECE302S13Boutin|Normalizing the probability mass function of a Gaussian random variable]]2 KB (304 words) - 07:43, 23 February 2013
- [[Category:independent random variables]] ...e Problem]]: obtaining the joint pdf from the marginals of two independent variables =2 KB (394 words) - 12:03, 26 March 2013
- ...on_ECE302S13Boutin|Normalizing the probability mass function of a Gaussian random variable]] ...13Boutin|Obtaining the joint pdf from the marginal pdfs of two independent variables]]2 KB (337 words) - 06:28, 1 March 2013
- ...ind the pdf of a random variable Y defined as a function Y=g(X) of another random variable X. **[[Practice_Question_independence_ECE302S13Boutin|Determine if X and Y independent from their joint density]]2 KB (328 words) - 04:58, 9 March 2013
- ...particular, we obtain a formula for the pdf of a sum of independent random variables (namely, the convolution of their respective pdf's).2 KB (286 words) - 09:11, 29 March 2013
- [[Category:independent random variables]] = [[:Category:Problem solving|Practice Problem]]: Determine if X and Y are independent =2 KB (290 words) - 10:17, 27 March 2013
- [[Category:normal random variable]] be a two-dimensional Gaussian random variable with mean <math>\mu</math> and standard deviation matrix <math>\Si2 KB (273 words) - 03:22, 26 March 2013
