beta random variable


X is a beta random variable with parameters a and b if

fX(x)=xa-1(1-x)b-1β(a,b), x[0,1]

Parameters:

  • a>0

  • b>0

Syntax:

XBeta(a,b)

Notes:

  1. 1.

    X is used in many statistical models.

  2. 2.

    The function β:R×RR is defined as β(a,b)=01xa-1(1-x)b-1𝑑x. β(a,b) can be calculated as β(a,b)=Γ(a)Γ(b)Γ(a+b) (For information on the Γ function, see the gamma random variable)

  3. 3.

    E[X]=aa+b

  4. 4.

    Var[X]=ab(a+b+1)(a+b)2

  5. 5.

    MX(t) not useful

Title beta random variable
Canonical name BetaRandomVariable
Date of creation 2013-03-22 11:54:30
Last modified on 2013-03-22 11:54:30
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 11
Author mathcam (2727)
Entry type Definition
Classification msc 60-00
Synonym beta distribution