Introduction to Mathematical Probability

approximate arbitrary 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 Jacob Bernoulli Laplace's formula large numbers law of large Liapounoff's m₁ Markoff mathematical expectation mutually exclusive n games normally distributed number of games number of points number of successes obtain occur player polynomial positive number power series preceding Prob proba probabilités problem proof required probability respectively result satisfy Solution standard deviation stochastic variables sufficiently suppose tends theory of probability tickets total number Tshebysheff urn contains values variables X1 whence white balls ξι