Probability: An IntroductionClarendon Press, 1986 - 211 pagine This new undergraduate text offers a concise introduction to probability and random processes. Exercises and problems range from simple to difficult, and the overall treatment, though elementary, includes rigorous mathematical arguments. Chapters contain core material for a beginning course in probability, a treatment of joint distributions leading to accounts of moment-generating functions, the law of large numbers and the central limit theorem, and basic random processes. |
Sommario
Events and probabilities | 11 |
Discrete random variables | 23 |
Multivariate discrete distributions and independence | 36 |
Probability generating functions | 48 |
Distribution functions and density functions | 58 |
Multivariate distributions and independence | 82 |
Moments and moment generating functions | 102 |
The two main limit theorems | 124 |
Branching processes | 143 |
Random walks | 153 |
Random processes in continuous time | 168 |
Appendix Difference equations | 195 |
Remarks on the problems | 201 |
Reading list | 207 |
Parole e frasi comuni
amoeba arrival binomial distribution boundary condition branching process calculate called Cauchy distribution central limit theorem characteristic function coin continuous random variables countable cov(X deduce defined density function f(x difference equation discrete random variables distributed random variables distribution with mean distribution with parameter dx dy E(X² E(XY equals event space example Exercises expectation exponential distribution Find the probability function F fx(x gamma distribution geometric distribution given Gx(s Hence independent random variables joint density function joint mass function large numbers Let X1 mean and variance mean square moment generating function Mx(t non-negative obtain outcome Oxford P(ANB particle Pk(t Poisson distribution Poisson process probability generating function probability space probability theory Problem process with rate Proof prove queue random walk real numbers S₁ satisfies Show simple random walk solution subsets Suppose taking values toss total number u₁ var(X variance o² X₁