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1. Markov chains - Yale University
probability distributions incorporate a simple sort of dependence structure, where the con- ... stochastic processes in an elementary setting. This classical subject is still very much alive, ... One answer is to say that it is a sequence {X0,X1,X2,...}of random variables that has the “Markov property”; we will discuss this in the next ...
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Chapter 1 Markov Chains - Yale University
www.stat.yale.eduChapter 1 Markov Chains ... chains are fundamental stochastic processes that have many diverse applica- ... what is the probability of reaching a certain state, ...
Chapter 9 Poisson processes - Yale University
www.stat.yale.eduA Poisson process with rate‚on[0;1/is a random mechanism that gener- ates “points” strung out along [0 ; 1 / in such a way that (i) the number of points landing in any subinterval of lengtht is a random variable with
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www.stat.yale.eduPage 1 Chapter 12 Multivariate normal distributions The multivariate normal is the most useful, and most studied, of the standard joint dis-tributions in probability.
Chapter 7 Continuous Distributions - Yale University
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Single-Stock Circuit Breakers - Yale University
www.stat.yale.eduThe single-stock circuit breakers will pause trading in any component stock of the Russell 1000 or S&P 500 Index in the event that the price of that stock has moved 10 percent or more in the preceding ve minutes. The pause generally will last ve minutes, and is intended to give the
Chapter 3 Total variation distance between measures
www.stat.yale.edu2 Chapter 3: Total variation distance between measures total variation distance has properties that will be familiar to students of the Neyman-Pearson approach to hypothesis testing. The Hellinger distance is closely related to the total variation distance—for example, both distances define
The bigmemory Package: Handling Large Data Sets in R …
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Seminar Notes: The Mathematics of Music - Yale University
www.stat.yale.eduUnderstanding Musical Sound 1.1 Sound, the human ear, and the sinusoidal wave 1.1.1 Sound waves and musical notation Music is organized sound, and it is from this standpoint that we begin our study. In the world of Western music, notation has been developed to describe music in a very precise way. Consider, for instance, the following lines of ...
Chapter 10 Joint densities - Yale University
www.stat.yale.eduand Y have continuous distributions, it becomes more important to have a systematic way to describe how one might calculate probabilities of the form Pf.X;Y/2Bgfor various sub- ... blobs, small shapes that don’t have any particular name—whatever suits the needs of a par-ticular calculation. <10.2> Example.
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