Introduction to Mathematical Probability |
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A₁ approximate arbitrary B₁ B₂ ball drawn Bernoulli's theorem black balls cards characteristic function compound probability consider continued fraction convergent definition denote distribution function divergence coefficient double integral E(xi equal equation event expression find the probability finite formula frequency given Hence independent trials independent variables inequality integer integral interval ith trial Jacob Bernoulli Laplace's formula large numbers law of large Liapounoff's m₁ mathematical expectation mutually exclusive n games normally distributed number of games number of points number of successes obtain occur P₁ player polynomial positive number power series preceding Prob proba probabilités problem proof required probability respectively result Solution stochastic variables sufficiently suppose tends theory of probability tickets total number Tshebysheff urn contains values variables x1 whence white balls