## A First Course in ProbabilityThe third edition earmarks the great success of this text among the students as well as the teachers. To enhance its utility one additional appendix on "The Theory of Errors" has been incorporated along with necessary modifications and corrections in the text. The treatment, as before, is rigorous yet impressively elegant and simple. The special feature of this text is its effort to resolve many outstanding confusions of probability and statistics. This will undoubtedly continue to be a valuable companion for all those pursuing a career in Statistics. |

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### Contents

Section 1 | 1 |

Section 2 | 4 |

Section 3 | 6 |

Section 4 | 49 |

Section 5 | 52 |

Section 6 | 54 |

Section 7 | 80 |

Section 8 | 89 |

Section 18 | 219 |

Section 19 | 231 |

Section 20 | 238 |

Section 21 | 243 |

Section 22 | 258 |

Section 23 | 282 |

Section 24 | 286 |

Section 25 | 305 |

Section 9 | 102 |

Section 10 | 104 |

Section 11 | 140 |

Section 12 | 147 |

Section 13 | 148 |

Section 14 | 160 |

Section 15 | 184 |

Section 16 | 188 |

Section 17 | 200 |

Section 26 | 367 |

Section 27 | 384 |

Section 28 | 462 |

Section 29 | 465 |

Section 30 | 468 |

Section 31 | 472 |

Section 32 | 481 |

Section 33 | 484 |

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### Common terms and phrases

absolutely continuous assume ball is drawn Bernoulli Bernoulli trials black balls Boole's inequality called Cauchy distribution characteristic function Chebyshev's Chebyshev's inequality chosen at random coefficient conditional distribution conditional p.d.f. continuity point converges countable defined Definition denoted density discrete distribution function easy to verify equally event exists Find the distribution Find the p.d.f. Find the probability function F given Hence the required i-th Ill Example implies independent random variables inequality integer interval joint p.d.f. Lemma Let F Let X follow lim inf lim sup linear matrix mean nonnegative normal distribution Note order statistics otherwise P(Xn pairwise pairwise independent parameters probability space prove r-th random vector regression Remark required probability sample space sequence subset total number transformation trials variance white ball WLLN