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1. Markov chains - Yale University
Section 4. Statement of the Basic Limit Theorem about conver-gence to stationarity. A motivating example shows how compli-cated random objects can be generated using Markov chains. Section 5. Stationary distributions, with examples. Probability flux. Section 6. Other concepts from the Basic Limit Theorem: ir-reducibility, periodicity, and ...
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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 12 Multivariate normal distributions - Yale University
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The bigmemory Package: Handling Large Data Sets in R …
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Chapter 7 Continuous Distributions - Yale University
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Single-Stock Circuit Breakers - Yale University
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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
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 12 Conditional densities
www.stat.yale.eduConditional densities 12.1Overview Density functions determine continuous distributions. If a continuous distri-bution is calculated conditionally on some information, then the density is called a conditional density. When the conditioning information involves another random variable with a continuous distribution, the conditional den-
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
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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