Suppose that we are to obtain a single observation Y from an exponential distribution with mean theta.
a) Find the distribution of U = Y/theta? Is U a pivotal quantity?
b) Use U = Y/theta and the pivotal method, to form a confidence interval formula for theta with a confidence level of 90%.
I know that the exponential distribution is:
f(x) = (1/theta) * e^(-x/theta)
What I'm confused about is how to find a distribution of U = Y/theta and if it is a pivotal quantity. Any help would be appreciated.