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     2  ~ 2013 dec 26independent random variablesIndependent random variables - Statlect, the digital textbookTwo random variables are independent if they convey no information about each other and, as a consequence, receiving information about one of the two does  ...
     4  ~ 2013 dec 06probability mass functionProbability mass function - StatLectThe distribution of a discrete random variable can be characterized through its probability mass function ( pmf ). The probability that a given number will be the  ...
     9  -2 2013 dec 29fundamentals of statisticsFundamentals of statistics - Statlect, the digital textbookFundamentals of statistics . Learn the mathematical foundations of statistics, through a series of rigorous but accessible lectures on the most frequently utilized  ...
     9  +1 2013 dec 07probability mass function exampleIn formal terms, the probability mass function of a discrete random variable X ... Example . Suppose a random variable X can take only three values (1, 2 and 3),  ...
     21  +11 2014 jan 29random vector generationJoint moment generating function - StatLectAs an example, we derive the joint mgf of a standard multivariate normal random vector . Example Let X be a Kx1 standard multivariate normal random vector .
     22  -9 2013 dec 16formula for conbinationsCombinations - StatLectCombinations with and without repetition, Definition and intuitive explanation. Counting combinations . Binomial coefficient. Examples .
     23  +20 2014 jan 07chi square excelChi - square distribution values - StatLectHow to compute values of the chi - square distribution using tables or computer programs such as Excel and Matlab.
     26  -8 2013 dec 15concept of probabilityProbability - StatLectWe then discuss the properties that probability needs to satisfy. Finally, we mention some possible interpretations of the concept of probability . Ω. In this lecture  ...
     34  +29 2014 feb 26expected valueExpected value - StatLectExpected value . The concept of expected value of a random variable is one of the most important concepts in probability theory. It was first devised in the 17th  ...
     34  -23 2014 jan 08chi square distributionChi - square distribution - StatLectThe Chi - square distribution explained, with examples, solved exercises and detailed proofs of important results.
     35  +26 2014 feb 25convergesMean square convergence - StatLectis said to converge to X in mean-square if [eq1] converges to X according to the metric [eq4] defined as follows: [eq5] (if you do not understand what it means "to  ...
     35  ~ 2014 jan 05chi color lineChi -square distribution plots - StatLectthe first graph (red line ) is the probability density function of a Chi -square ... Plots the grid for x for j=xtick line ('xData',[j j],'yData',ylimit,' color ',[0.75 0.75 0.75]  ...
     38  +48 2014 mar 04probability and statisticsStatlect, the digital textbook on probability and statisticsThe digital textbook on probability and statistics . Statlect is a free digital textbook on probability theory and mathematical statistics. Explore its main sections.
     39  +10 2014 feb 28poisson distributionPoisson distribution - StatLectThe Poisson distribution explained, with examples, solved exercises and detailed proofs of important results.
     48  +14 2014 jan 10probability sample spaceDefinitions and explanations of event, sample space , outcome, realized outcome, probability , probability measure, probability space, properties of probability .
     48  +53 2014 jan 05independent variable definitionIndependent random variables - StatLectThis lecture provides a formal definition of independence and discusses how to verify whether two or more random variables are independent .
     51  -17 2013 dec 16sites like wikipediaHow Wikipedia could make the world an even better place - StatLectThis short post explains how websites like Wikipedia could help solve important computational problems by harnessing the computational power of their  ...
     54  -16 2014 mar 04law of large numbersLaws of Large Numbers - Statlect, the digital textbookDefinition of Law of Large Numbers . Weak Law. Strong Law. Chebyshev's Weak Law. Proofs. Exercises.
     57  +3 2014 mar 07maximum likelihood estimationNormal distribution - Maximum likelihood estimationMaximum likelihood estimation of the parameters of the normal distribution. Derivation and properties, with detailed proofs.
     59  ~ 2014 mar 07theory of probabilityRead a rigorous yet accessible introduction to the main concepts of probability theory , such as random variables and random vectors, expected value, variance,   ...
     60  -12 2013 dec 31normal distribution tableNormal distribution values - Statlect, the digital textbookHow to compute values of the normal distribution using tables or computer programs such as Excel and Matlab.
     63  -31 2014 feb 13maximum likelihoodNormal distribution - Maximum likelihood estimation - StatLect
     67  -13 2014 jan 11probability density function examplesMarginal probability density function - StatLectThis is called marginal probability density function , in order to distinguish it from ... Example . Let X be a $2 imes 1$ absolutely continuous random vector having  ...
     69  ~ 2014 jan 05property numerics meaningsWe then discuss the properties that probability needs to satisfy. Finally, we mention some possible interpretations of the concept of probability. ... Six numbers , from 1 to 6, can appear face up, but we do not yet know which one of them will  ...
     70  ~ 2014 feb 28normal distribution assumptionsCentral Limit Theorem - StatLectis large enough, then a standard normal distribution is a good approximation of the ... So, roughly speaking, under the stated assumptions , the distribution of the   ...
     73  ~ 2014 feb 28likelihood probabilityMaximum likelihood - StatLectThis lecture deals with an estimation method called maximum likelihood (or maximum ... that we use to make statements about the probability distribution that   ...
     74  -14 2014 feb 21a legitimateLegitimate probability mass functions - StatLectWe prove not only that any probability mass function satisfies these two properties, but also that any function satisfying these two properties is a legitimate   ...
     76  -10 2014 feb 13correlation theoremCentral Limit Theorem for correlated sequences - Proof - StatLectThis page sketches some ideas for a proof of a Central Limit Theorem for correlated sequences. This is preliminary and exploratory. Let [eq1] be a sequence of  ...
     77  ~ 2014 jan 13generate terms of useMoment generating function - StatLectMoment generating function: definition, existence, moments, other
     80  ~ 2014 jan 14real numbers definitionLimit of a sequence - StatLectConvergence of a sequence of real numbers . Convergence of a generic sequence of objects: definition and intuitive explanation. Subsequences, metrics   ...
     81  ~ 2014 feb 16root mean squared errorPoint estimation - StatLectwhen the squared error is used as a loss function, then the risk [eq26] is called mean squared error ( MSE ). The square root of the mean squared error is called  ...
     88  -2 2014 feb 17central limit theoremA Central Limit Theorem (CLT) is a proposition stating a set of conditions that are sufficient to guarantee the convergence of the sample mean Xbar_n  ...
     90  ~ 2014 feb 08matlab convolution of continus functionSums of independent random variables - StatLectWe explain first how to derive the distribution function of the sum and then how to derive its probability mass function (if the summands are discrete ) or its  ...
     96  +5 2014 feb 28variance calculator formulateCovariance formula - StatLectGlossary entry for the term: covariance formula . StatLect. Lectures on Probability and Statistics.
     97  ~ 2014 feb 11root mean square errorwhen the squared error is used as a loss function, then the risk [eq26] is called mean squared error (MSE). The square root of the mean squared error is called  ...
     99  -56 2013 dec 11we value conceptTo keep things simple, we provide an informal definition of expected value and we discuss its computation in this lecture, while we relegate a more rigorous  ...
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