The distribution of speeds of molecules in thermal equilibrium as given by
statistical mechanics. The probability and cumulative distributions are

(1) | |||

(2) |

where is an incomplete Gamma Function and . The moments are

(3) | |||

(4) | |||

(5) | |||

(6) |

and the Mean, Variance, Skewness, and Kurtosis are

(7) | |||

(8) | |||

(9) | |||

(10) |

**References**

Spiegel, M. R. *Theory and Problems of Probability and Statistics.* New York: McGraw-Hill, p. 119, 1992.

von Seggern, D. *CRC Standard Curves and Surfaces.* Boca Raton, FL: CRC Press, p. 252, 1993.

© 1996-9

1999-05-26