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     2  ~ 2014 apr 14independent 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 mar 27probability 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 ...
     7  +2 2014 mar 29probability 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  +25 2014 apr 25chi square distributionChi - square distribution - StatLectThe Chi - square distribution explained, with examples, solved exercises and detailed proofs of important results.
     9  ~ 2014 apr 16fundamentals 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 ...
     12  +22 2014 jun 10expected 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 ...
     15  +48 2014 may 24maximum likelihoodMaximum likelihood - StatlectThis lecture deals with an estimation method called maximum likelihood (or maximum likelihood estimation - MLE). Before reading this lecture you should be  ...
     20  +19 2014 jun 16poisson distributionPoisson distribution - Statlect, the digital textbookThe Poisson distribution explained, with examples, solved exercises and detailed proofs of important results.
     22  +13 2014 jun 05convergesMean 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 ...
     23  ~ 2014 apr 25chi square excelChi - square distribution values - StatLectHow to compute values of the chi - square distribution using tables or computer programs such as Excel and Matlab.
     25  +32 2014 jul 02maximum likelihood estimationNormal distribution - Maximum likelihood estimation - StatlectMaximum likelihood estimation of the parameters of the normal distribution. Derivation and properties, with detailed proofs.
     25  -4 2014 may 10random 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 .
     30  -4 2014 apr 04concept of probabilityProbability - StatLectSince we usually speak of the " probability of an event", the next section introduces a formal definition of the concept of event. We then discuss the properties that ...
     35  +66 2014 apr 06statistics lecture notesStatlect, the digital textbook on probability and statisticsStatlect is a free digital textbook on probability theory and mathematical statistics . Explore its main sections. Fundamentals of probability theory. Read a rigorous ...
     35  -13 2014 apr 05formula for conbinationsCombinations - StatLectCombinations with and without repetition, Definition and intuitive explanation. Counting combinations . Binomial coefficient. Examples .
     39  ~ 2014 jun 09mean square errorMean squared error - StatLectIn the theory of point estimation, the mean squared error is frequently used to assess the risk of an estimator, that is, how large are on average the losses ...
     40  +33 2014 jun 11likelihood 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  ...
     41  -3 2014 jun 30probability 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.
     41  ~ 2014 jun 13javascript wikipediaHow Wikipedia could make the world an even better place - StatLectThis short post explains how websites like Wikipedia could help solve important ... It would suffice to add a piece of Javascript code to every Wikipedia page.
     41  +58 2014 apr 01we 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 ...
     42  ~ 2014 may 24حل 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 ...
     47  +4 2014 apr 05sites like wikipediaThis short post explains how websites like Wikipedia could help solve important computational problems by harnessing the computational power of their ...
     48  +28 2014 may 22correlation 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 ...
     50  +17 2014 apr 30probability 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 ...
     51  -16 2014 apr 23chi 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] ...
     58  ~ 2014 may 06distribution of textbooksStatlect is a free digital textbook on probability theory and mathematical statistics. ... Explore this compendium of common probability distributions , including the ...
     60  +41 2014 jun 10exercise 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 ...
     66  -12 2014 jun 16law of large numbersLaws of Large Numbers - StatLectDefinition of Law of Large Numbers . Weak Law. Strong Law. Chebyshev's Weak Law. Proofs. Exercises.
     69  +5 2014 may 29a legitimateLegitimate probability density functions - StatLectLegitimate probability density functions. This lecture discusses two properties characterizing probability density functions (pdfs). Not only any pdf satisfies these  ...
     71  ~ 2014 may 18check if function is defineNot only any pdf satisfies these two properties, but also any function that satisfies these two properties is a
     72  -3 2014 apr 24property numerics meaningsWe then discuss the properties that probability needs to satisfy. ... Six numbers , from 1 to 6, can appear face up, but we do not yet know which one of them .... clarify the meaning of probability, they all touch upon important aspects of probability.
     78  +10 2014 may 26central 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 ...
     78  -18 2014 apr 19normal distribution tableNormal distribution values - StatLectHow to compute values of the normal distribution using tables or computer programs such as Excel and Matlab.
     80  ~ 2014 may 20determinant 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].
     83  -35 2014 apr 29probability sample spaceDefinitions and explanations of event, sample space , outcome, realized outcome, probability , probability measure, probability space, properties of probability .
     87  -17 2014 jun 12normal distribution assumptionsis large enough, then a standard normal distribution is a good approximation of the ... So, roughly speaking, under the stated assumptions , the distribution of the  ...
     94  -4 2014 may 18matlab 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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