- #1

Phox

- 37

- 0

## Homework Statement

Let θ>0 and X

_{1}, X

_{2},...,X

_{n}be a random sample from the distribution with the pdf

f

_{x}(x)=f

_{x}(x;θ)=(θ/(2√x))e

^{-θ√x}, x>0

Recall:

Ʃ√x

_{i}, i=1, n has Gamma (α = n, "usual θ" = 1/θ) distribution.

a) Suggest a confidence interval θ with (1-α)100% confidence level.

b) Suppose n = 5, x

_{1}=5, x

_{2}=11, x

_{3}=2, x

_{4}=7, x

_{5}=3. Use part (a) to construct at 95% confidence interval for θ.

## Homework Equations

## The Attempt at a Solution

attempting to mimic what my professor did on a similar problem..

a)

b)

So

1) Is my work correct?

2) I don't understand why Ʃ√xi is relevant here

3) I don't understand the relationship between gamma and chi

^{2}distributions

Appreciate it.