- #1

- 8

- 0

## Homework Statement

Let X

_{1}, X

_{2},....X

_{n}be a random sample from the distribution with probability density function

f

_{X}(x;θ) = (θ+1)(1-x)

^{θ}, 0<x<1 θ>-1

a) What is the probability distribution of Y= -[itex]\sum ln(1-X

_{i}[/itex] from i=1 -> n

b) Suggest a (1-α)100% confidence interval for θ based on Y= -[itex]\sum ln(1-X

_{i}[/itex] from i=1 -> n

## Homework Equations

## The Attempt at a Solution

a) I began by transforming the equation.

Y= -Ʃ ln(1-X

_{i}) from i=1 -> n= -ln((1-X

_{i})

^{n}

e

^{Y}= 1/(1-X

_{i})

^{n}

X

_{i}=1-e

^{-Y/n}

f

_{y}(y) = f

_{x}(g

^{-1}(y)) [itex]\frac{dx}{dy}[/itex]

=[itex]\frac{(θ+1}{n}[/itex] e

^{=[itex]\frac{Y}{n}[/itex](θ+1)}

I don't think this is the correct answer. I'm not even sure if my math or the method to solving this is even correct.

b) I'm not even sure what they're asking for this part of the question. Could someone please clarify what I'm suppose to do after I find the probability distribution?

Thanks in advance.