Probability: Theory and ExamplesThomson Brooks/Cole, 2005 - 497 páginas Explains the fundamentals of probability, with multiple real-world examples for students new to this discipline. The problems range from easy to difficult, allowing students to tackle more complicated problems as their competence increases. |
Conteúdo
Markov Chains | 5 |
Central Limit Theorems | 77 |
8 Infinitely Divisible Distributions | 159 |
Direitos autorais | |
28 outras seções não mostradas
Termos e frases comuns
Applying B₁ Borel-Cantelli lemma central limit theorem ch.f Chapter characteristic function Chebyshev's inequality complete the proof compute conclude continuous countable define definition density desired result follows disjoint distribution F distribution function distribution with mean dominated convergence theorem ergodic EX₁ EX² Example EXERCISE finite Fn(x formula Fubini's theorem gives inequality inf{n integral irreducible large numbers last result law of large Lebesgue measure let Sn Let X1 lim inf lim sup log log Markov chain Markov property martingale normal distribution o-field observe P(An P(Sn P(X₁ P(Xn permutation Poisson distribution Poisson process probability measure Proof Let random variables random walk recurrent Remark renewal right-hand side Section Show simple random walk Sn/n stable law submartingale Suppose X1 trivial variance weak law X₁ Xn,m Y₁