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# Topic: Expected value

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 Encyclopedia: Expected value This estimates the true expected value in an unbiased manner and has the property of minimizing the sum of the squares of the residuals (the sum of the squared differences between the observations and the estimate). The expected value of a statistic is therefore the mean of the sampling distribution of the statistic. Expected values of variables are indicated by an "E" with the variable enclosed in brackets. www.nationmaster.com /encyclopedia/Expected-value   (505 words)

 Facts about topic: (Expected value)   (Site not responding. Last check: 2007-10-22) The expected values of the powers of are called the moment (A particular point in time) s of ; the moments about the mean (additional info and facts about moments about the mean) of are expected values of powers of. To empirically estimate the expected value of a random variable, one repeatedly measures observations of the variable and computes the arithmetic mean (The sum of the values of a random variable divided by the number of values) of the results. Expected value is also a key concept in economics (The branch of social science that deals with the production and distribution and consumption of goods and services and their management) and finance (The commercial activity of providing funds and capital). www.absoluteastronomy.com /encyclopedia/e/ex/expected_value.htm   (854 words)

 [No title] The expected value of a random variable is analogous to the mean of a list: It is the balance point of the probability histogram, just as the mean is the balance point of the histogram of the list. The expected value of a negative binomial random variable with parameters p and r is r/p. The expected value of the sample sum of n random draws with or without replacement from a box of numbered tickets is n times the mean of the numbers on all the tickets in the box, including duplicates as often as they occur. www.stat.berkeley.edu /users/stark/SticiGui/Text/ch13.htm   (4863 words)

 Expected value - Open Encyclopedia   (Site not responding. Last check: 2007-10-22) If something happens that is not at all expected it is a surprise. In general, if X is a random variable defined on a probability space (Ω, P), then the expected value EX of X (sometimes denoted $\langle\left\{\right\}X\rangle\right) is defined as$ The expected values of the powers of X are called the moments of X; the moments about the mean of X are expected values of powers of $X-EX.$ open-encyclopedia.com /Expected_value   (595 words)

 Expected value - LearnThis.Info Enclyclopedia   (Site not responding. Last check: 2007-10-22) Note that not all random variables have an expected value, since the integral may not exist. Two variables with the same probability distribution will have the same expected value. The expected values of the powers of X are called the moments of X; the moments about the mean of X are also defined as certain expected values. encyclopedia.learnthis.info /e/ex/expected_value.html   (486 words)

 Glossary   (Site not responding. Last check: 2007-10-22) The expected value of the chance variation is zero; the standard error of the chance variation is the same as the standard error of the random variable---the size of a "typical" difference between the random variable and its expected value. The mean squared error of an estimator of a parameter is the expected value of the square of the difference between the estimator and the parameter. The expected value of the sample percentage from a simple random sample or a random sample with replacement is the population percentage. stat-www.berkeley.edu /~stark/SticiGui/Text/gloss.htm   (13841 words)

 Expected Volume and Value of Structural Dimension Lumber from   (Site not responding. Last check: 2007-10-22) Given the data on weighted average unit value (in $/mbf or$/cu.m.) and the estimated total volume of dimension lumber per acre, it was then possible to estimate the total value of dimension lumber per acre of loblolly pine plantation of a given age. The expected value of stress-graded dimension lumber produced per acre of loblolly pine plantation of a given age was estimated by multiplying the values given by Equations 2 and 3. The expected yield values were used in an incremental analysis in conjunction with discounted-cash-flow techniques to determine the economic desirability of deferring the harvesting of a loblolly pine plantation stand of a given age for purposes of producing structural dimension lumber. www.alabamaforestowners.com /CILive/CI0206_a.htm   (3764 words)

 PokerTips.org - Poker Strategy - Expected Value It is because of a concept known as expected value. Expected value is your expected return on a wager. Expected value is another reason why you should never play in a poker game that you cannot afford. www.pokertips.org /strategy/expected-value.php   (839 words)

 Mean, Variance and Distributions In addition, it is assumed that the values are drawn from a sample distribution taken from a larger population., and that the variance and standard deviation of the population are to be estimated. where p(x) is proportional to the probability that the actual value will equal x; ev and sd stand for the expected value and standard deviation, respectively, of the distribution, and nd is the deviation of x from ev in standard deviation units. For example, the expected shortfall is the expected value of the shortfall, whether there is one or not. www.stanford.edu /~wfsharpe/mia/rr/mia_rr1.htm   (3358 words)

 expected value   (Site not responding. Last check: 2007-10-22) When we say expected value of X is 2.5, E(X)=2.5, we are not saying that 2.5 is the most probable value of X. In fact, X may never be equal to 2.5. For example if X denotes the number obtained in a roll of a fair die, then the expected value of X is 3.5. The expected value of X depends on the probability of a fire p. math.gmu.edu /~tlim/expect.htm   (297 words)

 NetLogo Models Library: Expected Value Thus, the term 'expected value' may be defined as the sum of the products of the value of each possible event and the probability of that possible event. The calculation first determines the value of the 'average tile' and then multiplies this value by the number of tiles in the kid's sample (how many tiles the kid flips). The relative ratios of the various marble sets are determined by relative values of all of the sliders on the left. ccl.northwestern.edu /netlogo/models/ExpectedValue   (2221 words)

 3.7 Value Functions Notice the negative values near the lower edge; these are the result of the high probability of hitting the edge of the grid there under the random policy. The value of a state is the negative of the number of strokes to the hole from that location. The value of a state depends on the the value of the actions possible in that state and on how likely each action is to be taken under the current policy. www.cs.ualberta.ca /~sutton/book/3/node8.html   (1741 words)

 Statistics Glossary - random variables and probability distributions The expected value (or population mean) of a random variable indicates its average or central value. Stating the expected value gives a general impression of the behaviour of some random variable without giving full details of its probability distribution (if it is discrete) or its probability density function (if it is continuous). The expected value of a random variable X is symbolised by E(X) or µ. www.stats.gla.ac.uk /steps/glossary/probability_distributions.html   (2101 words)

 Goodness of Fit Test by Excel   (Site not responding. Last check: 2007-10-22) I used cells B7-B9 for the expected proportions, C7-C9 for the observed values and D7-D9 for the expected frequency. To find the value of each cell in the new table we should multiply the sum of the cell column by the sum of the cell row and divide the results by the grand total. For example to find the expected value for the cell C5 which is replaced in c11 you could click on the formula bar and enter C6*D5/D6 then enter in cell C11. www.ubalt.edu /arc/math_resources/stat_goodoffittest.html   (986 words)

 Expected Value Expected value is one of the fundamental concepts in probability, in a sense more general than probability itself. The expected value of a real-valued random variable gives a measure of the center of the distribution of the variable. More importantly, by taking the expected value of various functions of a general random variable, we can measure many interesting features of its distribution, including spread and correlation. www.math.uah.edu /stat/expect   (106 words)

 Properties of Expected Value We now know that the expected value of a random variable gives the center of the distribution of the variable. By finding expected values of various functions of a random vector, we can measure many interesting features of the distribution of the vector. The expected value of a random variable X is based, of course, on the probability measure P for the experiment. www.fmi.uni-sofia.bg /vesta/Virtual_Labs/expect/expect2.html   (936 words)

 SurfStat.australia It also illustrates the concept of the expected value of a random variable. What is E(X), the expected number of males in the group, and what is the variance of X? Assume X ~ binomial (5,0.5). Expected Value and Variance for a Function of Random Variables www.anu.edu.au /nceph/surfstat/surfstat-home/3-2-5.html   (655 words)

 3.7 Value Functions Almost all reinforcement learning algorithms are based on estimating value functions--functions of states (or of state-action pairs) that estimate how good it is for the agent to be in a given state (or how good it is to perform a given action in a given state). It states that the value of the start state must equal the (discounted) value of the expected next state, plus the reward expected along the way. Exercise 3.12 The value of a state depends on the the values of the actions possible in that state and on how likely each action is to be taken under the current policy. www.cs.ualberta.ca /~sutton/book/ebook/node34.html   (1585 words)

 Expected Value (Expectation or Mean) We denote the expected value (expectation or mean) of X as either It represents the (probability-weighted) average value for the random variable. The concept of expected value generalizes to multiple dimensions. www.riskglossary.com /articles/mean.htm   (259 words)

 [No title] We say that there is symmetry around 1.5 since, in a real sense, it is the number in the center and the different values of X fluctuate around it. The variance of a probability distribution is a measure not of its central value but of the dispersion around the expected value. It is a measure of how "spread out" the X values are around the center or expected value. www.spelman.edu /~jstone/e203/evvarhdt.html   (423 words)

 Course Prerequisites   (Site not responding. Last check: 2007-10-22) Expected value is the fundamental principle of decision analysis. The concept is thought to have first originated in the 17th century. Expected Value: the probability-weighted average of all possible outcomes of a chance event. www.maxvalue.com /ev.htm   (132 words)

 [No title] The expected value of obtaining perfect information on all the uncertain parameters gives ‘overall EVPI’, whereas ‘Partial EVPI’ is the expected value of learning the true value(s) of an individual parameter or of a subset of the parameters. We mathematically define partial EVPI using expected value notation, assess the alternative computation methods and algorithms, investigate the mathematical conditions when the alternative computation approaches may be used, and use case studies to demonstrate the accuracy or otherwise of ‘short-cut’ algorithm approximations. Secondly, in the inner loop it is important that values of (c are sampled from their conditional distribution, conditional on the values for (i that have been sampled in the outer loop. www.tonyohagan.co.uk /academic/other/EVPI.doc   (8216 words)

 Statistics Glossary - Probability Relative frequency is another term for proportion; it is the value calculated by dividing the number of times an event occurs by the total number of times an experiment is carried out. The expected value of a random variable X is symbolised by E() or u. The simplest case of the normal distribution, known as the Standard Normal Distribution, has expected value zero and variance one. www.cas.lancs.ac.uk /glossary_v1.1/prob.html   (3540 words)

 The expected value of the free residual   (Site not responding. Last check: 2007-10-22) The expected value of the sum of squared residuals associated with the excluded observations is then obtained by taking matrix traces. From equation (1) the expected value of the residual associated with these observations at convergence is given by In the linear approximation, both expressions for the expected value are independent of the observations (structure amplitudes and restraints). www.biochem.ucl.ac.uk /~roman/rfree/node9.html   (229 words)

 [No title]   (Site not responding. Last check: 2007-10-22) Expected Values Intuitively, the expected value of a random variable is the average value of the random variable. This means that if we repeat the relevant experiment many times, and compute the actual value of X each time, and compute the average of the values of X, the result will be close to E(X); and furthermore, if we keep repeating the experiment more times, the successive averages will converge to E(X). Expected value of a function of a random variable Suppose X is a discrete random variable, and Y is another random variable that is defined in terms of X, say by Y = h(X). www.chesco.com /~marys/math/M205/notes3.doc   (2401 words)

 BBC Education - AS Guru - Maths - Methods - Probability Distributions - Expected Value How can we say what a reasonable expectation is? If we refer to probability, then the probability of winning the National Lottery is about 1/14 000 000 and the probability of being struck by lightening is about 1/5 000 000. Investment companies expect an 'average' return on their portfolios. Expectation theory is a way of giving a measure to our long term expected outcomes of uncertain events. www.bbc.co.uk /education/asguru/maths/12methods/07distributions/35expected/index.shtml   (179 words)

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