Notes on Random Variables , Expectations , Probability Densities , and MartingalesSims, Christopher
4.A.Leon-Garcia,ProbabilityandRandomProcessesforElectricalEngineering,Addison- Wesley,2ndEdition,1994. 5.H.StarkandJ.W.Woods,ProbabilityandRandomProcesseswithApplicationstoSignal Processing3rdEd.,Prentice-Hall,EnglewoodCliffs,NJ,2001. 6.P.Z.Peebles,Probability,RandomVariables,andRandomSignalPrinciples,3rd.Ed...
另可参考Probability and Measure, 3rd Edition by Patrick Billingsley和Feller的卷二. Dudley本人在MIT的本科课18.440 Probability and Random Variables用的是Ross的本科教材,另外Degroot的教材也是本科通用的。 评分☆☆☆ 据说上课的notes很多是借鉴这本书的,课上没有涉及的内容在别处也多少接触过,所以允许我为了...
Let us now return to our example involving boxes of fruit. For the moment, we shall once again be explicit about distinguishing between the random variables and their instantiations. We have seen that the probabilities of selecting either the red or the blue boxes are given by , and , respec...
we will consider parameters and measurement errors to be random variables whose statis- tical properties or distributions we wish to infer using measured data. The classical probability space provides the basis for defining and illustrating these concepts. Definition 4.1 (Probability Space). A pr...
Probability mass function(p.m.f) of random variable X is a function Joint probability mass functionof X and Y is a function Cumulative distribution function(c.d.f) of a random variable X is a function: The c.d.f describes the probability in a specific interval, whereas the p.m.f desc...
As mentioned at the beginning of Chapter 3, the two important types of random variables are discrete and continuous. In this chapter, we study the second general type of random variable that arises in many applied problems. Sections 4.1 and 4.2 present the basic definitions and properties of co...
Probability inequalities for sums of bounded random variables Journal of the American Statistical Association, 58 (1963), pp. 13-30 Google Scholar [15] Ch. Huygens, Van Rekeningh in Spelen van Geluck, 1656–1657. Reprinted in vol. XIV of [16] Google Scholar [16] Ch. Huygens Œuvres com...
random experiment sample sample random variables expected value independence variance mean let us discuss these terms one by one. random experiment an experiment whose result cannot be predicted, until it is noticed is called a random experiment. for example, when we throw a dice randomly, the ...
CourseOutline(CBreferstochaptersintheCasellaandBergerbook,G referstochaptersinGoldberger) 1.ProbabilityTheory (a)ElementaryProbabilityTheory(CB1.1–1.2) (b)ConditionalProbability,Independence(CB1.3) (c)RandomVariables,DistributionFunctions,FunctionsofRandom Variables(CB1.4–1.6,2.1) (d)JointDistributions, Condi...