An Introduction to Probability and Random Processes by Gian-Carlo Rota, Kenneth Baclawski

By Gian-Carlo Rota, Kenneth Baclawski

Read Online or Download An Introduction to Probability and Random Processes PDF

Similar probability books

Advanced Stochastic Models, Risk Assessment, and Portfolio Optimization: The Ideal Risk, Uncertainty, and Performance Measures (Frank J. Fabozzi Series)

This groundbreaking booklet extends conventional techniques of hazard dimension and portfolio optimization via combining distributional types with danger or functionality measures into one framework. all through those pages, the professional authors clarify the basics of likelihood metrics, define new methods to portfolio optimization, and speak about numerous crucial threat measures.

Seminar on Stochastic Analysis, Random Fields and Applications V: Centro Stefano Franscini, Ascona, May 2004: v. 5

This quantity includes twenty-eight refereed study or overview papers awarded on the fifth Seminar on Stochastic procedures, Random Fields and purposes, which happened on the Centro Stefano Franscini (Monte VeritÃ ) in Ascona, Switzerland, from may possibly 30 to June three, 2005. The seminar centred in most cases on stochastic partial differential equations, random dynamical structures, infinite-dimensional research, approximation difficulties, and monetary engineering.

Probability in Social Science: Seven Expository Units Illustrating the Use of Probability Methods and Models, with Exercises, and Bibliographies to Guide Further Reading in the Social Science and Mathematics Literatures

Birkhauser Boston, Inc. , will post a sequence of rigorously chosen mono­ graphs within the region of mathematical modeling to give severe functions of arithmetic for either the undergraduate and the pro viewers. many of the monographs to be chosen and released will charm extra to the pro mathematician and person of arithmetic, helping familiarize the person with new versions and new tools.

Additional resources for An Introduction to Probability and Random Processes

Example text

Further, a probability of any event E consisting of t outcomes, equals P {E} = ωk ∈E 1 n =t 1 n = number of outcomes in E . 21. Tossing a die results in 6 equally likely possible outcomes, identified by the number of dots from 1 to 6. 5), we obtain, P {1} = 1/6, P { odd number of dots } = 3/6, P { less than 5 } = 4/6. ♦ The solution and even the answer to such problems may depend on our choice of outcomes and a sample space. 5) does not apply. 22. A card is drawn from a bridge 52-card deck at random.

7 Chebyshev’s inequality . . . . . . . . . . . . . . . . . 8 Application to finance . . . . . . . . . . . . . . . . . . 4 Families of discrete distributions . . . . . . . . . . . . . . . . . 1 Bernoulli distribution . . . . . . . . . . . . . . . . . . 2 Binomial distribution . . . . . . . . . . . . . . . . . . 3 Geometric distribution . . . . . . . . . . . . . . .

4 Variance and standard deviation . . . . . . . . . . . . 5 Covariance and correlation . . . . . . . . . . . . . . . 6 Properties . . . . . . . . . . . . . . . . . . . . . . . . 7 Chebyshev’s inequality . . . . . . . . . . . . . . . . . 8 Application to finance . . . . . . . . . . . . . . . . . . 4 Families of discrete distributions . . . . . . . . . . . . . . . . . 1 Bernoulli distribution .