ELementary Probability Theory with Stochastic Processes |
Common terms and phrases
A₁ apply arbitrary argument Axiom ball drawn binomial binomial coefficients black balls calculus called cards Chapter coin compute conditional probability consider converges countable course defined definition density function discussed disjoint drawing equal equation event Example expected number Find finite follows formula given Hence Hint independent random variables infinite integers large numbers law of large m₁ Markov chain Markov property mathematical means multinomial distribution n₁ namely normal distribution notation obtain outcomes P(X₁ P{X₁ p₁ pair particle permutations Poisson distribution Poisson process possible probability distribution probability measure probability theory problem proof Proposition random walk real numbers recurrent red balls replaced result S₁ sample point sample space sequence step stochastic subset Suppose T₁ tion tokens tossed total number transition matrix trials X₁ X₂ zero