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• Convergence_of_random_variables wikiPageWikiLinkText "convergence of random variables".
• Convergence_of_random_variables wikiPageWikiLinkText "convergence of sets of random variables".
• Convergence_of_random_variables wikiPageWikiLinkText "convergence".
• Convergence_of_random_variables wikiPageWikiLinkText "convergent".
• Convergence_of_random_variables wikiPageWikiLinkText "converges in distribution".
• Convergence_of_random_variables wikiPageWikiLinkText "converges in law".
• Convergence_of_random_variables wikiPageWikiLinkText "converges in probability".
• Convergence_of_random_variables wikiPageWikiLinkText "converges".
• Convergence_of_random_variables wikiPageWikiLinkText "in distribution".
• Convergence_of_random_variables wikiPageWikiLinkText "in probability".
• Convergence_of_random_variables wikiPageWikiLinkText "limit in probability".
• Convergence_of_random_variables wikiPageWikiLinkText "mean square".
• Convergence_of_random_variables wikiPageWikiLinkText "mean".
• Convergence_of_random_variables wikiPageWikiLinkText "probabilistic limit theorems".
• Convergence_of_random_variables wikiPageWikiLinkText "see here".
• Convergence_of_random_variables wikiPageWikiLinkText "statistical convergence".
• Convergence_of_random_variables wikiPageWikiLinkText "tends".
• Convergence_of_random_variables wikiPageWikiLinkText "this property".
• Convergence_of_random_variables wikiPageWikiLinkText "weakly".
• Convergence_of_random_variables bodystyle "width: 28em;".
• Convergence_of_random_variables data "As grows larger, this distribution will gradually start to take shape more and more similar to the bell curve of the normal distribution. If we shift and rescale appropriately, then will be converging in distribution to the standard normal, the result that follows from the celebrated central limit theorem.".
• Convergence_of_random_variables data "As the factory is improved, the dice become less and less loaded, and the outcomes from tossing a newly produced die will follow the uniform distribution more and more closely.".
• Convergence_of_random_variables data "Consider a man who tosses seven coins every morning. Each afternoon, he donates one pound to a charity for each head that appeared. The first time the result is all tails, however, he will stop permanently.".
• Convergence_of_random_variables data "Consider an animal of some short-lived species. We record the amount of food that this animal consumes per day. This sequence of numbers will be unpredictable, but we may be quite certain that one day the number will become zero, and will stay zero forever after.".
• Convergence_of_random_variables data "However, when we consider any finite number of days, there is a nonzero probability the terminating condition will not occur.".
• Convergence_of_random_variables data "Let be the fraction of heads after tossing up an unbiased coin times. Then has the Bernoulli distribution with expected value and variance . The subsequent random variables will all be distributed binomially.".
• Convergence_of_random_variables data "Let X1, X2, … be the daily amounts the charity received from him.".
• Convergence_of_random_variables data "Note that does not converge almost surely however. No matter how professional the archer becomes, there will always be a small probability of making an error. Thus the sequence {Xn} will never turn stationary: there will always be non-perfect scores in it, even if they are becoming increasingly less frequent.".
• Convergence_of_random_variables data "Suppose is an iid sequence of uniform random variables. Let be their sums. Then according to the central limit theorem, the distribution of approaches the normal distribution. This convergence is shown in the picture: as grows larger, the shape of the pdf function gets closer and closer to the Gaussian curve. center|200px".
• Convergence_of_random_variables data "Suppose a new dice factory has just been built. The first few dice come out quite biased, due to imperfections in the production process. The outcome from tossing any of them will follow a distribution markedly different from the desired uniform distribution.".
• Convergence_of_random_variables data "Suppose a person takes a bow and starts shooting arrows at a target. Let Xn be his score in n-th shot. Initially he will be very likely to score zeros, but as the time goes and his archery skill increases, he will become more and more likely to hit the bullseye and score 10 points. After the years of practice the probability that he hit anything but 10 will be getting increasingly smaller and smaller and will converge to 0. Thus, the sequence converges in probability to X = 10.".
• Convergence_of_random_variables data "This example should not be taken literally. Consider the following experiment. First, pick a random person in the street. Let X be his/her height, which is ex ante a random variable. Then you start asking other people to estimate this height by eye. Let be the average of the first n responses. Then by the law of large numbers, the sequence Xn will converge in probability to the random variable X.".
• Convergence_of_random_variables data "We may be almost sure that one day this amount will be zero, and stay zero forever after that.".
• Convergence_of_random_variables datastyle "text-align: left;".
• Convergence_of_random_variables header "Archer".
• Convergence_of_random_variables header "Dice factory".
• Convergence_of_random_variables header "Example 1".
• Convergence_of_random_variables header "Example 2".
• Convergence_of_random_variables header "Graphic example".
• Convergence_of_random_variables header "Height of a person".
• Convergence_of_random_variables header "Tossing coins".
• Convergence_of_random_variables headerstyle "background-color: lightblue; text-align: left; padding-left: 3pt;".
• Convergence_of_random_variables headerstyle "background-color: lightblue; text-align:left;".
• Convergence_of_random_variables title "Examples of almost sure convergence".
• Convergence_of_random_variables title "Examples of convergence in distribution".
• Convergence_of_random_variables title "Examples of convergence in probability".
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• Convergence_of_random_variables subject Category:Convergence_(mathematics).
• Convergence_of_random_variables subject Category:Probability_theory.
• Convergence_of_random_variables subject Category:Statistical_theory.
• Convergence_of_random_variables subject Category:Stochastic_processes.
• Convergence_of_random_variables type Type.
• Convergence_of_random_variables type Function.
• Convergence_of_random_variables type Process.
• Convergence_of_random_variables type Redirect.
• Convergence_of_random_variables type Source.
• Convergence_of_random_variables type Theory.
• Convergence_of_random_variables type Type.
• Convergence_of_random_variables comment "In probability theory, there exist several different notions of convergence of random variables. The convergence of sequences of random variables to some limit random variable is an important concept in probability theory, and its applications to statistics and stochastic processes.".
• Convergence_of_random_variables label "Convergence of random variables".
• Convergence_of_random_variables sameAs Q578985.
• Convergence_of_random_variables sameAs Konvergenz_(Stochastik).
• Convergence_of_random_variables sameAs Konbergentzia_estokastiko.
• Convergence_of_random_variables sameAs Convergence_de_variables_aléatoires.
• Convergence_of_random_variables sameAs התכנסות_(הסתברות).
• Convergence_of_random_variables sameAs Convergenza_di_variabili_casuali.
• Convergence_of_random_variables sameAs 確率変数の収束.
• Convergence_of_random_variables sameAs 확률변수의_수렴.
• Convergence_of_random_variables sameAs Convergentie_(kansrekening).
• Convergence_of_random_variables sameAs Zbieżność_według_rozkładu.
• Convergence_of_random_variables sameAs Convergência_de_variáveis_aleatórias.
• Convergence_of_random_variables sameAs m.0ddg4.
• Convergence_of_random_variables sameAs Збіжність_випадкових_величин.
• Convergence_of_random_variables sameAs Sự_hội_tụ_của_các_biến_ngẫu_nhiên.
• Convergence_of_random_variables sameAs Q578985.
• Convergence_of_random_variables sameAs 随机变量的收敛.
• Convergence_of_random_variables wasDerivedFrom Convergence_of_random_variables?oldid=704327320.
• Convergence_of_random_variables depiction Convergence_in_distribution_(sum_of_uniform_rvs).gif.
• Convergence_of_random_variables isPrimaryTopicOf Convergence_of_random_variables.

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