Also known as Bernoulli's Theorem. Let , ..., be a sequence of independent and identically distributed
random variables, each having a Mean
and Standard Deviation . Define a new variable

(1) |

(2) |

(3) |

Therefore, by the Chebyshev Inequality, for all ,

(4) |

(5) |

Stated another way, if an event occurs times in Trials and if is the probability of success in a single Trial, then the probability that for an arbitrary Positive quantity approaches 1 as .

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1999-05-26