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Sample Space and Probability p
General Random Variables p
Further Topics on Random Variables p
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aperiodic approximation arrival assume balance equations Bernoulli process calculate coin conditional expectation conditional PDF conditional probability Consider continuous random variable corresponding defined denoted derive discrete random variable disjoint E[XY end-of-chapter problems equal event Example expected value exponential random variable exponentially distributed Figure finite number formula function fx(x fy(y geometric given independent random variables inequality integer interarrival interval joint PDF large numbers law of large limit theorem linear Markov chain mean and variance multiplication rule nonnegative normal random variables Note number of elements obtain packet Poisson PMF Poisson process possible outcomes probabilistic model probability law result roll sample space Show single recurrent class slot Solution squares estimator standard normal steady-state probabilities student subset success toss total expectation theorem total number total probability theorem transform associated transient Transition probability graph trials uniformly distributed var(X variable with parameter verify zero