(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

1. The Beta distribution: A Beta random variable is a positive continuous random variable

dened on [0; 1] that has two parameters associated with it, usually denoted and . Both

and must be positive real numbers. The beta distribution is used to model the probability

of success in Bernoulli trials when each trial has a random success probability - e.g. tossing

randomly selected coins.

The density function of a beta random variable X with parameters [itex]\alpha[/itex] and [itex]\beta[/itex] is

for 0 < x < 1.

The Beta distribution gets its name from the fact that its density function involves the so-called

Beta function. Here are several facts about the Beta function B(s; t):

(a) Let X be Beta with arbitrary parameters and . Show how to use the facts above

about the Beta function to derive c.

(b) Use the fact above about the Beta function and the facts from Homework 6 about the

Gamma function to find E(X) and E(X^{2})

) without actually doing any integration yourself.

Check your answers against Wikipedia

2. Relevant equations

don't know of any

3. The attempt at a solution

don't know where to start either of these

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Question about Beta distribution (probability)

**Physics Forums | Science Articles, Homework Help, Discussion**