# How do I calculate Confidence Interval for Gamma Distributed Pivotal Quantity?

I'm studying confidence intervals and then I came across the following problem:

It's said that a random variable X has Skewed Exponencial Distribution with parameters $$\alpha >0$$ and $$v \in \mathbb{R}$$ when $$\alpha (X - v)\text{~}Exp(1)$$. Suppose $$X_1,X_2,...,X_{20}, Y_1,Y_2,...,Y_{20}$$ iid following a Skewed Exponencial distribution with parameters $$\alpha > 0\text{ and } v$$, both unknown.

a) Let $$W_k:=Y_k - X_k, k=1,2,...,20$$. Find $$E(W_1), Var(W_1) \text{ and } E(W_1^2)$$.

b) Let $$Q := \alpha|W_1| + ... + \alpha|W_{20}|$$ Prove that Q is a pivot.

c) Find the Bilateral Confidence Interval for $$\alpha$$, with covering probability equal 95% based on Q.

I could solve A and B, but I have no idea how to handle c. Does anybody may help me?