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## Homework Statement

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

## Homework Equations

don't know of any

## The Attempt at a Solution

don't know where to start either of these