By Dimitri P. Bertsekas
ISBN-10: 188652940X
ISBN-13: 9781886529403
An intuitive, but special advent to chance idea, stochastic strategies, and probabilistic types utilized in technology, engineering, economics, and similar fields. this is often the presently used textbook for "Probabilistic structures Analysis," an introductory chance direction on the Massachusetts Institute of know-how, attended via loads of undergraduate and graduate scholars. The publication covers the basics of likelihood idea (probabilistic types, discrete and non-stop random variables, a number of random variables, and restrict theorems), that are commonly a part of a primary path at the topic. It additionally includes, a few extra complex subject matters, from which an teacher can decide to fit the ambitions of a selected path. those issues contain transforms, sums of random variables, least squares estimation, the bivariate common distribution, and a reasonably special advent to Bernoulli, Poisson, and Markov methods. The booklet moves a stability among simplicity in exposition and class in analytical reasoning. the various extra mathematically rigorous research has been simply intuitively defined within the textual content, yet is constructed intimately (at the extent of complex calculus) within the quite a few solved theoretical difficulties. The ebook has been greatly followed for school room use in introductory chance classes in the united states and in a foreign country.
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Additional info for Introduction to Probability
Sample text
In addition, we will provide examples of some important and frequently encountered random variables. In Chapter 3, we will discuss general (not necessarily discrete) random variables. Even though this chapter may appear to be covering a lot of new ground, this is not really the case. ) and apply them to random variables rather than events, together with some appropriate new notation. The only genuinely new concepts relate to means and variances. 2 PROBABILITY MASS FUNCTIONS The most important way to characterize a random variable is through the probabilities of the values that it can take.
We have illustrated through examples three methods of specifying probability laws in probabilistic models: (1) The counting method. This method applies to the case where the number of possible outcomes is finite, and all outcomes are equally likely. To calculate the probability of an event, we count the number of elements in the event and divide by the number of elements of the sample space. (2) The sequential method. This method applies when the experiment has a sequential character, and suitable conditional probabilities are specified or calculated along the branches of the corresponding tree (perhaps using the counting method).
What is the probability that each group includes a graduate student? 3, but we will now obtain the answer using a counting argument. We first determine the nature of the sample space. A typical outcome is a particular way of partitioning the 16 students into four groups of 4. We take the term “randomly” to mean that every possible partition is equally likely, so that the probability question can be reduced to one of counting. According to our earlier discussion, there are 16 4, 4, 4, 4 = 16! 4! 4!
Introduction to Probability by Dimitri P. Bertsekas
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