## Random Processes: A First Look, Second Edition,This book develops appreciation of the ingenuity involved in the mathematical treatment of random phenomena, and of the power of the mathematical methods employed in the solution of applied problems. It is intended to students interested in applications of probability to their disciplines. |

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### Contents

Easy Life and Good Times | 1 |

Probability | 2 |

Life Times | 9 |

Prolongation of Life Times | 22 |

Bus Problem | 29 |

Combinations of Life Times | 34 |

Extreme Life Times | 45 |

Great Expectations | 51 |

Accidents Just Happen | 157 |

Problems | 165 |

TO Renew or Not to Renew | 187 |

Renewals | 188 |

Renewal Equation | 195 |

Jumping Rabbit | 206 |

Problems | 214 |

Markovian Dance | 231 |

Double Scotch | 67 |

How Normal Is Normal? | 75 |

When in Doubt Approximate | 85 |

Problems | 91 |

Be Discreet with Discrete | 131 |

Bernoulli Trials | 132 |

Applications of Binomial | 141 |

Geometric Waiting Time | 146 |

Poisson Distribution | 152 |

Poisson Input | 233 |

It Is Easy to Learn | 241 |

OnOff Transitions | 248 |

Queueing | 256 |

Inference from Interference | 341 |

Appendix A Formulae | 393 |

Appendix B Tables | 399 |

Suggestions for Further Reading | 405 |

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### Common terms and phrases

applications approximately arrivals assume average cost binomial busy calculations called Chapter clearly common compute conditional Consider constant continuous corresponding cost function customers defined denote density f depends differentiation discussed distribution equal equation estimator evaluate event exactly Example exponential expression finite fixed formula given graph Hence increases independent individual infinite initial instant integral interest interval joint jumps known Laplace transform length limit lines mathematical mean method needed Note Observe obtained occur operation parameter period Pij(t Poisson distribution positive present probability problem queue random variable relation renewal represents respectively result sample sample mean Section Show simple situation solution Statistical success Suppose theory tion transition trials variance Verify waiting write yields zero