A Distribution given by

(1) | |||

(2) |

The distribution of heads and tails in Coin Tossing is a Bernoulli distribution with . The Generating Function of the Bernoulli distribution is

(3) |

(4) | |||

(5) | |||

(6) | |||

(7) |

and the Moments about 0 are

(8) | |||

(9) | |||

(10) |

The Moments about the Mean are

(11) | |||

(12) | |||

(13) |

The Mean, Variance, Skewness, and Kurtosis are then

(14) | |||

(15) | |||

(16) | |||

(17) |

To find an estimator for a population mean,

(18) |

so is an Unbiased Estimator for . The probability of successes in trials is then

(19) |

(20) |

© 1996-9

1999-05-26