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apply assumed balls Bernoulli trials binomial distribution bivariate table calculation called Chapter coefficients coin conditional Consider continuous busy period convolution corresponding counting distribution defined definition density function diagonal discrete and continuous distributed with parameter distribution function equal equilibrium probabilities Erlang process example expression Find the probability finite formula gamma distribution geometric distribution important independent infinite number interval Laplace transform Laplace-Stieltjes transform Markov chain mathematical mixed discrete negative binomial negative binomial distribution negative exponentially distributed non-negative integers normalization to unity notation number of arrivals number of customers obtained Poisson distribution Poisson process positive integers possible probabilistic probability distribution probability generating function problem proof px(t queueing theory random walk range renewal process result sample points sample space server service period Show simple stationary vector Stieltjes integration Stochastic Processes student Suppose Theorem tion transition matrix values variance written zero