Probability TheoryAllied Publishers, 2013 Probability theory |
المحتوى
Independence of events and sequences of trials | 12 |
Random variables | 24 |
Expectation | 30 |
Variance | 40 |
Higher moments and inequalities for deviations | 46 |
The Law of Large Numbers Limit Theorems | 50 |
De MoivreLaplace theorems | 60 |
Generating Functions and Random Walks | 70 |
Covariance analysis and multivariate normal distribution | 157 |
Convergence of distributions | 163 |
Comparison of distributions | 181 |
Conditional Distributions | 200 |
Conditional expectations with respect to σalgebras | 217 |
Some Kinds of Dependence | 226 |
Martingales | 233 |
Markov chains | 243 |
Foundations of the Theory | 88 |
Probability distributions | 120 |
Random variables | 141 |
Some particular distributions on the real line | 144 |
Limit Theorems | 260 |
A Regularly varying functions Limit theorems for identically | 270 |
طبعات أخرى - عرض جميع المقتطفات
عبارات ومصطلحات مألوفة
A₁ A₂ absolutely continuous arbitrary b₁ b₂ Borel sets C₁ C₂ called Cauchy distribution ch.f characteristic function conditional expectation consider convergence Corollary corresponding countable defined Definition degenerate distribution denote distribution F distribution function elementary event equal Example exists F(dr F(dx F(dz F₁ finite formula function F(x holds identically distributed implies independent r.v.'s inequality integral interval large numbers law of large Lebesgue integral Lebesgue measure Lemma Let F Limit theorems matrix nonnegative normal distribution o-algebra P₁ P₂ parameter Poisson distribution probability measure probability space Proof of Theorem prove r.vec random vector reader is invited real line relation representation respect right-hand side S₁ Section segment sequence set-function space stable distributions standard normal Subsection sufficiently summands symmetric uniformly valid values variance X₁ X₂ Y₁ Y₂