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2  ~ 2014 aug 06independent random variablesIndependent random variables - StatLectTwo 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  ~ 2014 jul 19probability 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 ...
5  +4 2014 aug 08fundamentals of statisticsFundamentals of statistics - StatLectFundamentals of statistics . Learn the mathematical foundations of statistics, through a series of rigorous but accessible lectures on the most frequently utilized ...
6  +1 2014 jul 21probability 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), ...
9  +3 2014 sep 27expected 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 ...
10  -1 2014 aug 17chi square distributionChi - square distribution - StatlectThe Chi - square distribution explained, with examples, solved exercises and detailed proofs of important results.
11  +4 2014 sep 15maximum likelihoodMaximum likelihood - StatlectThis lecture deals with an estimation method called maximum likelihood (or maximum likelihood estimation - MLE). Before reading this lecture you should be  ...
14  +11 2014 oct 04maximum likelihood estimation
15  +15 2014 jul 28concept of probabilityFundamentals of probability - StatlectThis is an introduction to the main concepts of probability theory. After reading the lectures, test your knowledge with the multiple choice tests in the last section.
17  +8 2014 aug 31random 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 .
17  +6 2014 aug 16chi square excelChi - square distribution values - StatlectHow to compute values of the chi - square distribution using tables or computer programs such as Excel and Matlab.
22  +18 2014 sep 26likelihood probabilityThis lecture deals with an estimation method called maximum likelihood (or maximum ... that we use to make statements about the probability distribution that  ...
22  +28 2014 aug 21probability density function examplesProbability density function - StatlectFor example , in the picture below the blue line is the pdf of a normal random ... Example . Suppose a random variable X has probability density function [eq5].
26  -6 2014 sep 29poisson distributionPoisson distribution - StatlectThe Poisson distribution explained, with examples, solved exercises and detailed proofs of important results.
26  +52 2014 aug 11normal distribution tableNormal distribution values - StatlectHow to compute values of the normal distribution using tables or computer programs such as Excel and Matlab.
37  +14 2014 aug 15chi 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] ...
37  +10 2014 jul 29sites 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 ...
38  -3 2014 jul 29formula for conbinationsCombinations - StatlectCombinations with and without repetition, Definition and intuitive explanation. ... The following is a useful recursive formula for computing binomial coefficients: ...
50  -8 2014 sep 15حل الدوالGamma function - Exercise Set 1 - StatlectThis exercise set contains some solved exercises on the Gamma function . The theory needed to solve these exercises is introduced in the lecture entitled ...
50  +51 2014 aug 21generate terms of useMoment generating function - StatlectMoment generating function: definition, existence, moments, other
51  -29 2014 sep 24convergesMean 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 ...
53  +13 2014 sep 29law of large numbersLaws of Large Numbers - StatlectDefinition of Law of Large Numbers . Weak Law. Strong Law. Chebyshev's Weak Law. Proofs. Exercises.
55  -14 2014 oct 02probability and statisticsStatlect, the digital textbookThe digital textbook on probability and statistics . Statlect is a free digital textbook on probability theory and mathematical statistics. Explore its main sections.
56  -8 2014 sep 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 ...
59  +1 2014 sep 27exercise centralCentral Limit Theorem - Exercise Set 1 - StatLectThis exercise set contains some solved exercises on the Central Limit Theorem. The theory needed to solve these exercises is introduced in the lecture entitled ...
61  +40 2014 sep 08hypothesis testingHypothesis testing - StatLectTest of hypothesis , null hypothesis , alternative hypothesis , critical region, test statistic, power function, size of a test .
66  +14 2014 sep 11determinant of an infinite matrixPrecision matrix - StatlectGlossary entry for the term: precision matrix . ... tends to infinity , we have zero precision; on the contrary, when variance tends to zero, we have infinite precision . ... because, by elementary properties of the determinant , we have that [eq6].
66  -31 2014 jul 29statistics lecture notesThe digital textbook on probability and statistics . Statlect is a free digital textbook on probability theory and mathematical statistics . Explore its main sections.
76  -7 2014 sep 20a legitimateLegitimate probability density functions - StatlectLegitimate probability density functions. This lecture discusses two properties characterizing probability density functions (pdfs). Not only any pdf satisfies these  ...
77  ~ 2014 jul 26six sigma algebraConditional probability as a random variable - StatlectSix numbers (from 1 to \$6)\$ .... More details. Conditioning with respect to sigma - algebras ... smallest \$ sigma \$ - algebra containing all the events \$Hin ciFourier \$  ...
79  +4 2014 aug 20probability sample spaceProbability - StatlectDefinitions and explanations of event, sample space , outcome, realized outcome, probability , probability measure, probability space, properties of probability .
80  -2 2014 sep 17central limit theoremCentral Limit Theorem - StatlectA 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 ...
82  +19 2014 aug 24real 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  ...
85  +16 2014 jul 27used computer valuesHow to compute values of the normal distribution using tables or computer programs such as ... A fact that is often used in calculations is the following: [eq5].
88  +13 2014 sep 26variance calculator formulateCovariance - StatlectCovariance : definition, intuition, computation, proofs, exercises. ... The following covariance formula is often used to compute the covariance between two ...
91  +3 2014 sep 09matlab 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 ...
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