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- ...obability of one proposition given that another proposition holds. For the probability of proposition A given proposition B, we write P(A|B).</p> ...)</math> and <math>P(\lnot A \cap B)</math>. Therefore, we must divide the probability we are looking for, <math>P(A \cap B)</math>, by the sum of all probabiliti1 KB (245 words) - 12:18, 17 March 2008
- #redirect: [[Conditional probability_Old Kiwi]]47 B (5 words) - 12:19, 17 March 2008
- ...[Category:probability]] [[Category:problem solving]][[Category:conditional probability]]770 B (129 words) - 08:10, 28 January 2013
- [[ECE600_F13_probability_spaces_mhossain|Previous Topic: Probability Spaces]]<br/> [[Category:probability]]6 KB (1,023 words) - 12:11, 21 May 2014
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- What is the expression for the probability of getting at least one trial with no outliers given <math>N</math> trials? * Let <math>\epsilon</math> be the probability that a data element is an ''outlier''14 KB (2,253 words) - 12:21, 9 January 2009
- ...is tricky because we don't care about the probability that Bob WON but the probability that he has won on his second turn GIVEN the fact that he won at all. Therefore, we need to calculate the conditional probability.1 KB (223 words) - 02:41, 18 February 2009
- * [[Conditional PDFs - random breaking of a stick, Lec 15 on 10/6_ECE302Fall2008sanghavi]] * [[Example for continuous Probability Distributions. Vivek_ECE302Fall2008sanghavi]]5 KB (663 words) - 13:02, 22 November 2011
- Bob, Carol, Ted and Alice take turns (in that order) tossing a coin with probability of tossing a Head, <math>P (H) = p</math>, where <math>0 < p < 1</math>. Th ...ne of its faces is randomly looked at. It turns out to be red. What is the probability the other face of the SAME card is ALSO red?3 KB (555 words) - 12:54, 22 November 2011
- Since the product of the two probabilities is equal to overall probability, the events are independent. ==Conditional Probability==977 B (158 words) - 13:00, 22 November 2011
- The theorem of total probability states that <math>P(A) = P(A|C)P(C) + P(A|C^c)P(C^c)</math>. Show that thi ...s are down on the same day. How large should <math>k</math> be so that the probability total outage occurs at least one day in a year is less than or equal to 0.06 KB (998 words) - 12:55, 22 November 2011
- Tip: Just expand the right hand side by using the conditional probability and simplify.88 B (14 words) - 08:06, 13 September 2008
- ...be complicated easily because what we have to deal with is the conditional probability in the second roll. ...t I must calculate as each possibility of second roll times first red roll probability.731 B (116 words) - 07:07, 15 September 2008
- ...(Red1), P(Red1 Red2), and P(Red1 Red2 Red3). From this values, We can find conditional probabilty of each case.254 B (47 words) - 08:35, 16 September 2008
- '''Sample Space, Axioms of probability (finite spaces, infinite spaces)''' '''Properties of Probability laws'''3 KB (525 words) - 13:04, 22 November 2011
- Probability of getting heads given a particular coin q is: ...g the above answers into the conditional probability formula will give the probability of H2|H1.449 B (89 words) - 10:33, 18 October 2008
- ...andom variables, we can do this. We don't have to worry about finding the conditional PDF of Q given H1, making this pretty easy.333 B (64 words) - 10:26, 20 October 2008
- Here are some concepts taught in class about conditional probability which can be useful to solve the problem. Some of us have given the procedu ...bability of any event A given the event X = 0, and also of the conditional probability of A given the event X = 1. The former is denoted P(A|X = 0) and the latter2 KB (332 words) - 16:52, 20 October 2008
- Pick hypothesis that maxes conditional PDF Probability of Type I : Pr(x E R|H0)489 B (102 words) - 10:56, 3 December 2008
- Pick hypothesis that maxes conditional PDF Probability of Type I : Pr(x E R|H0)687 B (125 words) - 13:43, 22 November 2011
- *I believe the definition of the conditional expectation on page 8 is not true, possibly what was meant was: <math>E[X|Y ...nts regarding the lab, I want to correct my stated results. To recap, the conditional from which <math>W</math> was drawn should indeed depend on the neighborhoo3 KB (543 words) - 12:55, 12 December 2008
- ...one out of so many theorems. However, Bayes' theorem which I learned in my probability class is one of these that dazzles me. I especially like its alternative fo ...re events from sample space S: P(F)!=0, P(E)!=0. P(F|E) is the conditional probability of F given E. P(E), P(F) are marginal probabilities of E and F respectively713 B (137 words) - 07:32, 31 August 2008
- ===Conditional Probability=== This problem can be solved using conditional probability. Once the door is opened, you have some extra information.11 KB (1,998 words) - 12:45, 24 September 2008
- ...E''' and '''F''' are events in '''S''' (sample space) the the conditional probability of '''E''' and '''F''' is '''P(E|F) = P(E intersect F)'''. the conditional probability of "E" given "F" is =<math> \frac {P(EnF)}{P(F)}</math>860 B (130 words) - 08:16, 20 May 2013
- ...he solution usually given is that if you choose a door and not switch, the probability you were right is 1/3 -- there's one treasure door and 3 doors in total. ...ragon to treasure). There's two dragon doors and 3 doors in total, so this probability is 2/3.539 B (97 words) - 09:49, 7 October 2008
- Bayes' decision rule creates an objective function which minimizes the probability of error (misclassification). This method assumes a known distribution for ...an Parameter Estimation is a technique for parameter estimation which uses probability densities as estimates of the parameters instead of exact deterministic one31 KB (4,832 words) - 18:13, 22 October 2010
- * Parametric Estimation of Class Conditional Density The class conditional density <math>p(\vec{x}|w_i)</math> can be estimated using training data. W10 KB (1,488 words) - 10:16, 20 May 2013
- *Determining probability of a new point requires one calculation: P(x|theta) *Probabilistic (probability density) estimate of parameters, p(theta | Data)6 KB (995 words) - 10:39, 20 May 2013
- ...ty density function) and cdf (cumulative distribution function), or simply probability distribution function. The probability density function or pdf is defined as: <math>p({x}) = p(x_1,\cdots , x_n) =8 KB (1,360 words) - 08:46, 17 January 2013
- ...obability of one proposition given that another proposition holds. For the probability of proposition A given proposition B, we write P(A|B).</p> ...)</math> and <math>P(\lnot A \cap B)</math>. Therefore, we must divide the probability we are looking for, <math>P(A \cap B)</math>, by the sum of all probabiliti1 KB (245 words) - 12:18, 17 March 2008
- ...nd argument, holding the first fixed. Eg: consider a model which gives the probability density function of observable random variable X as a function of parameter708 B (126 words) - 01:55, 17 April 2008
- == Example of Turning Conditional Distributions Around == Suppose that the conditional distributions <math>P_{\mathbb{X}|\mathbb{Y}}</math> are empirically estima7 KB (948 words) - 04:35, 2 February 2010
- '''Topics Covered''': An introductory treatment of probability theory including distribution and density functions, moments and random var i. an ability to solve simple probability problems in electrical and computer engineering applications.2 KB (231 words) - 07:20, 4 May 2010
- Bayes' decision rule creates an objective function which minimizes the probability of error (misclassification). This method assumes a known distribution for ...an Parameter Estimation is a technique for parameter estimation which uses probability densities as estimates of the parameters instead of exact deterministic one31 KB (4,787 words) - 18:21, 22 October 2010
- [[Category:probability]] *[[Probability_Formulas|Probability Formulas]]2 KB (238 words) - 12:14, 25 September 2013
- [[Category:probability]] Question 1: Probability and Random Processes1 KB (191 words) - 17:42, 13 March 2015
- Find the conditional density of <math>\mathbf{Y}</math> conditioned on <math>\mathbf{X}=x</math> Find a maximum aposteriori probability estimator.7 KB (1,103 words) - 05:27, 15 November 2010
- What is the probability that this experiment terminates on or before the seventh coin toss? What is the probability that this experiment terminates with an even number of coin tosses?10 KB (1,827 words) - 08:33, 27 June 2012
- ...tion consists of two separate short questions relating to the structure of probability space: ...}P_{2}\left(A\right),\qquad\forall A\in\mathcal{F}</math> is also a valid probability measure on <math class="inline">\mathcal{F}</math> if <math class="inline"7 KB (1,210 words) - 08:31, 27 June 2012
- ...th> is the power set of <math class="inline">\mathcal{S}</math> , and the probability measure <math class="inline">\mathcal{P}</math> is specified by the pmf <m ...math class="inline">f_{\mathbf{X}}\left(x|\mathbf{Z}=z\right)</math> , the conditional pdf of <math class="inline">\mathbf{X}</math> given the event <math class=14 KB (2,358 words) - 08:31, 27 June 2012
- ..."inline">\mathbf{X}</math> is a binomial distributed random variable with probability mass function (pmf) given by <math class="inline">p_{n}\left(k\right)=\left ...random variables, with <math class="inline">\mathbf{X}_{n}</math> having probability mass function <math class="inline">p_{n}\left(k\right)=\left(\begin{array}{10 KB (1,754 words) - 08:30, 27 June 2012
- ...on values <math class="inline">0,1,2,\cdots</math> and having conditional probability mass function <math class="inline">p_{\mathbf{N}}\left(n|\left\{ \mathbf{X} Find the probability that \mathbf{N}=n .9 KB (1,560 words) - 08:30, 27 June 2012
- Find the conditional density of <math class="inline">\mathbf{Y}</math> conditioned on <math cla Find a maximum aposteriori probability estimator.2 KB (416 words) - 11:47, 3 December 2010
- [[Category:probability]] [https://www.projectrhea.org/learning/practice.php Practice Problems] on Probability7 KB (960 words) - 18:17, 23 February 2015
- ...ty density function) and cdf (cumulative distribution function), or simply probability distribution function. The probability density function or pdf is defined as: <math>p({x}) = p(x_1,\cdots , x_n) =8 KB (1,403 words) - 11:17, 10 June 2013
- * Parametric Estimation of Class Conditional Density The class conditional density <math>p(\vec{x}|w_i)</math> can be estimated using training data. W10 KB (1,472 words) - 11:16, 10 June 2013
- *Determining probability of a new point requires one calculation: P(x|theta) *Probabilistic (probability density) estimate of parameters, p(theta | Data)6 KB (976 words) - 13:25, 8 March 2012
- =Student Project for [[MA375]]: Mysteries of Probability= ...lity of an event, the more certain we are that the event will occur. Thus, probability in an applied sense is a measure of the confidence a person has that a (ran12 KB (2,113 words) - 06:50, 21 March 2013
- [[Category:probability]] Question 1: Probability and Random Processes5 KB (780 words) - 01:25, 9 March 2015
- [[Category:probability]] Question 1: Probability and Random Processes5 KB (735 words) - 01:17, 10 March 2015
- [[Category:probability]] Question 1: Probability and Random Processes4 KB (609 words) - 01:54, 10 March 2015
- [[Category:probability]] Question 1: Probability and Random Processes4 KB (572 words) - 10:24, 10 March 2015
- [[Category:probability]] Question 1: Probability and Random Processes5 KB (748 words) - 01:01, 10 March 2015
- [[Category:probability]] Probability, Statistics, and Random Processes for Electrical Engineering, 3rd Edition,10 KB (1,422 words) - 20:14, 30 April 2013
- *1.2 Probability Models **Probability Laws (axioms, properties4 KB (498 words) - 10:18, 17 April 2013
- ...y:ECE302Spring2013Boutin]] [[Category:ECE]] [[Category:ECE302]] [[Category:probability]] [[Category:problem solving]] [[Category:conditional probability]]1 KB (175 words) - 11:45, 28 January 2013
- ...Category:probability]] [[Category:problem solving]] [[Category:conditional probability]] =Conditional Probability Problem=1 KB (212 words) - 12:34, 27 January 2013
- ...probabilities can be used to obtain the probability of false alarm and the probability of missed detection in a detection experiment. **[[Practice_Question_Monty_Hall_ECE302S13Boutin|Use Conditional Probability to explain the solution of the Monty Hall Problem]]2 KB (336 words) - 08:08, 25 January 2013
- = [[:Category:Problem solving|Practice Problem on]] Conditional Probability = ...oncept of conditional probability to explain why switching door leads to a probability of success equal to 2/3.7 KB (1,241 words) - 13:49, 13 February 2013
- Invent a problem related to conditional probability and/or independence and solve it. Then post your problem and solution on a [[Category:probability]]3 KB (489 words) - 10:10, 4 February 2013
- ...Category:probability]] [[Category:problem solving]] [[Category:conditional probability]] =Practice Problem on Probability ( [[ECE302]] )=2 KB (279 words) - 12:39, 26 January 2013
- '''Conditional Probability''' One dice is rolled two separate times. Find the probability that the dice lands on an even number both times, and the sum of the two ro1 KB (143 words) - 19:18, 27 January 2013
- ...Category:probability]] [[Category:problem solving]] [[Category:conditional probability]] [[Category:independence]] (a) Assuming that we have an equal probability of sampling a pixel from each image (ie <math style='inline'>P(im_1) = P(im5 KB (779 words) - 19:36, 27 January 2013
- ...y:ECE302Spring2013Boutin]] [[Category:ECE]] [[Category:ECE302]] [[Category:probability]] [[Category:problem solving]] [[Category:conditional probability]]1 KB (181 words) - 11:47, 28 January 2013
- ...[Category:probability]] [[Category:problem solving]][[Category:conditional probability]]770 B (129 words) - 08:10, 28 January 2013
- ...int_1_ECE302_Spring2012_Boutin|invented a problem]] related to conditional probability and/or independence and solved it. We are inviting you to go over [[Bonus_p = Link to pages with student-created problems on conditional probability and/or independence =2 KB (361 words) - 11:13, 28 January 2013
- ...degree". We subsequently finished illustrating the concept of conditional probability for discrete random variables. We then covered the concept of independent d2 KB (321 words) - 11:12, 15 February 2013
- ...suming that the problems are posed in probabilistic terms and all relevant probability values are known (It is important to note that in reality its not always li ...bility ''P(x<sub>1</sub>)'' that the next card is diamonds, and some prior probability ''P(x<sub>2</sub>)'' that it is spades, and both probabilities sum up to 15 KB (844 words) - 23:32, 28 February 2013
- ...states exactly how costly each chosen action is, and is used to convert a probability determination into a decision. Cost functions enables us to look at situati ...<sub>j</sub>'', therefore by using Bayes formula we can find the posterior probability ''P''(''x<sub>j</sub>''|'''Y'''):5 KB (893 words) - 16:27, 1 March 2013
- ...ariables. We finished the lecture by giving the definition of conditional probability density function and illustrating it with an example. ::[[Practice_Question_probability_meeting_occurs_ECE302S13Boutin|Compute the probability that a meeting will occur]]2 KB (324 words) - 13:11, 5 March 2013
- [[Category:conditional density function]] = [[:Category:Problem_solving|Practice Problem]]: What is the conditional density function=1 KB (157 words) - 11:59, 26 March 2013
- [[Category:conditional density function]] = [[:Category:Problem_solving|Practice Problem]]: What is the conditional density function=1,022 B (148 words) - 12:00, 26 March 2013
- [[Category:conditional density function]] = [[:Category:Problem_solving|Practice Problem]]: What is the conditional density function=2 KB (299 words) - 09:17, 27 March 2013
- ...niform distribution on a circle of radius r. We also saw the definition of conditional density when the condition is an event B (instead of the event "random vari ...ice_Question_find_conditional_ellipse_ECE302S13Boutin|Find the conditional probability density function (again)]]3 KB (350 words) - 11:24, 6 March 2013
- *[[Practice_Question_probability_meeting_occurs_ECE302S13Boutin|Compute the probability that a meeting will occur]] ...ractice_Question_find_conditional_pdf_ECE302S13Boutin|Find the conditional probability density function]]2 KB (340 words) - 03:37, 27 March 2013
- [[Category:conditional probability]] <pre>keyword: probability, Bayes' Theorem, Bayes' Rule </pre>4 KB (649 words) - 13:08, 25 November 2013
- [[Category:probability]] What is the probability that the meeting will occur?3 KB (559 words) - 07:02, 22 March 2013
- ...on Theory, showing how conditional probabilities are used to determine the probability of a particular event given that we know the prior probabilities. For this ...an or not. Without the information about the length of the last names, the probability of a student being African would always be 0.4, but with the added feature,3 KB (415 words) - 18:34, 22 March 2013
- *[[Practice_Question_probability_meeting_occurs_ECE302S13Boutin|Compute the probability that a meeting will occur]] ...ractice_Question_find_conditional_pdf_ECE302S13Boutin|Find the conditional probability density function]]2 KB (333 words) - 18:02, 2 April 2013
- ...nbsp; Discriminant functions are used to find the minimum probability of error in decision making problems. In a problem with feature vector '''y ...ub>'' being the state of nature, and ''P''(''w<sub>j</sub>'') is the prior probability that nature is in state ''w<sub>j</sub>''. If we take p('''Y'''|''w<sub>i</5 KB (844 words) - 05:43, 13 April 2013
- [[Category:probability]] *[[ECE600_F13_probability_spaces_mhossain|Probability Spaces]]2 KB (227 words) - 12:10, 21 May 2014
- [[ECE600_F13_Conditional_probability_mhossain|Next Topic: Conditional Probability]] [[Category:probability]]20 KB (3,448 words) - 12:11, 21 May 2014
- [[ECE600_F13_probability_spaces_mhossain|Previous Topic: Probability Spaces]]<br/> [[Category:probability]]6 KB (1,023 words) - 12:11, 21 May 2014
- [[ECE600_F13_Conditional_probability_mhossain|Previous Topic: Conditional Probability]]<br/> [[Category:probability]]9 KB (1,543 words) - 12:11, 21 May 2014
- [[ECE600_F13_rv_conditional_distribution_mhossain|Next Topic: Conditional Distributions]] [[Category:probability]]15 KB (2,637 words) - 12:11, 21 May 2014
- [[Category:probability]] <font size= 3> Topic 7: Random Variables: Conditional Distributions</font size>6 KB (1,109 words) - 12:11, 21 May 2014
- [[ECE600_F13_rv_conditional_distribution_mhossain|Previous Topic: Conditional Distributions]]<br/> [[Category:probability]]9 KB (1,723 words) - 12:11, 21 May 2014
- [[Category:probability]] ==Conditional Expectation==8 KB (1,474 words) - 12:12, 21 May 2014
- [[Category:probability]] ...math>_Y</math> or pmf p<math>_Y</math> when Y = g(X), expectation E[g(X)], conditional expectation E[g(X)|M], and characteristic function <math>\Phi_X</math>. We8 KB (1,524 words) - 12:12, 21 May 2014
- [[Category:probability]] <font size= 3> Topic 15: Conditional Distributions for Two Random Variables</font size>6 KB (1,139 words) - 12:12, 21 May 2014
- [[Category:probability]] <font size= 3> Topic 16: Conditional Expectation for Two Random Variables</font size>4 KB (875 words) - 12:13, 21 May 2014
- [[Category:probability]] * The axioms of probability14 KB (2,241 words) - 10:42, 22 January 2015
- ...it is used to classify continuously valued data. Then we will present the probability of error that results from using Bayes rule. When Bayes rule is used the resulting probability of error is the smallest possible error, and therefore becomes a very impor13 KB (2,062 words) - 10:45, 22 January 2015
- ...ath>P(B)</math>. By the definition of the conditional probability, a joint probability of <math>A</math> and <math>B</math>, <math>P(A, B)</math>, is the product ...hese are what we already know. With these information, we can say that the probability that the person who he had a conversation with was a woman is19 KB (3,255 words) - 10:47, 22 January 2015
- In class we discussed Bayes rule for minimizing the probability of error. Our goal is to generalize this rule to minimize risk instead of probability of error.12 KB (1,810 words) - 10:46, 22 January 2015
- ...information provided by the training data to help determine both the class-conditional densities and the priori probabilities. ...th>x_1, x_2, ... , x_n</math> drawn independently according to the unknown probability density <math>p(x)</math>.8 KB (1,268 words) - 08:31, 29 April 2014
- ...side should be divided by Prob(x) according to the property of conditional probability. ii) The vertical axis of Fig. 2 is just labeled “histogram.” I would s2 KB (259 words) - 12:40, 2 May 2014
- ...variable which means <math>\theta' = w_{i}</math> is same as a posteriori probability <math>P(w_{i}|x').</math> If sample sizes are big enough, it could be assum ...lity of error as <math>P(e|x)</math>. Using this the unconditional average probability of error which indicates the average error according to training samples ca14 KB (2,313 words) - 10:55, 22 January 2015
- ...on the observation on above equations, it can be concluded that both class-conditional densities and the priori could be obtained based on the training data. ...<math>\theta</math> to be a vector (random variable). More specifically, a probability function given a class condition of D and a parameter vector of <math>\thet10 KB (1,625 words) - 10:51, 22 January 2015
- ...tions defined in the normal way, which is correct. As one might guess, the probability distributions that are used to map samples to classes are not always of imm ...ut a substantial amount of information about the distribution of data (and conditional distributions of data belonging to each class) it is near impossible to do16 KB (2,703 words) - 10:54, 22 January 2015
- ...of the data. Instead, it takes the data as given and tries to maximize the conditional density (Prob(class|data)) directly. ...the probability. We want to say that given a hair length is 10 inches, the probability of the person being a female is close to 1.9 KB (1,540 words) - 10:56, 22 January 2015
- ...that illustrates Bayes rule and how it can be used to update or revise the probability. Bayes Rule is an important rule in probability theory that allows to update or revise our theories when new evidence is gi7 KB (1,106 words) - 10:42, 22 January 2015
- First recall that the joint probability density function of <math>(\mathbf X,\theta)</math> is the mapping on <math Next recall that the (marginal) probability density function f of <math>X</math> is given by10 KB (1,600 words) - 10:52, 22 January 2015
- ...variable which means <math>\theta' = w_{i}</math> is same as a posteriori probability <math>P(w_{i}|x').</math> If sample sizes are big enough, it could be assum ...lity of error as <math>P(e|x)</math>. Using this the unconditional average probability of error which indicates the average error according to training samples ca14 KB (2,323 words) - 04:54, 1 May 2014
- ...variable which means <math>\theta' = w_{i}</math> is same as a posteriori probability <math>P(w_{i}|x').</math> If sample sizes are big enough, it could be assum ...lity of error as <math>P(e|x)</math>. Using this the unconditional average probability of error which indicates the average error according to training samples ca14 KB (2,340 words) - 17:24, 12 May 2014
- ...these parameters of the MEAN, the author goes on to derive the conditional probability of p(x|D) using the afore-mentioned parameters2 KB (300 words) - 17:04, 12 May 2014
- [[Category:probability]] Question 1: Probability and Random Processes1 KB (187 words) - 01:03, 10 March 2015
- [[Category:probability]] Question 1: Probability and Random Processes2 KB (366 words) - 01:36, 10 March 2015
- [[Category:probability]] Question 1: Probability and Random Processes4 KB (679 words) - 01:58, 10 March 2015
- [[Category:probability]] Question 1: Probability and Random Processes3 KB (454 words) - 10:25, 10 March 2015
- [[Category:probability]] Question 1: Probability and Random Processes2 KB (351 words) - 00:17, 4 December 2015
- [[Category:probability]] Question 1: Probability and Random Processes4 KB (851 words) - 23:04, 31 January 2016
- [[Category:probability]] Question 1: Probability and Random Processes3 KB (502 words) - 15:33, 19 February 2019
- ...“Stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event”. ...occurrence of S can be expressed as the multiplication of the conditional probability of occurrence of each word <math>w_{1}, w_{2}, ... w_{n}</math>. Therefore:8 KB (1,251 words) - 00:22, 6 December 2020
- ...ter obtaining new data. The theorem describes the conditional probability (probability of one event occurring with some relationship to one or more other events)654 B (101 words) - 20:50, 6 December 2020
- ...ter obtaining new data. The theorem describes the conditional probability (probability of one event occurring with some relationship to one or more other events)713 B (106 words) - 21:43, 6 December 2020
- ...ter obtaining new data. The theorem describes the conditional probability (probability of one event occurring with some relationship to one or more other events) ...lates the probability of the hypothesis before getting the evidence to the probability of the hypothesis after getting the evidence, making P(A) the prior and P(B1 KB (212 words) - 22:21, 6 December 2020
- Probability : Group 4 Probability14 KB (2,441 words) - 16:10, 14 December 2022
