Please solve all parts a-d. Please show all work and all steps. Please make sure work is clear. In order to get an upvote, please DO NOT use a former result.

Suppose that X1, ..., Xn is a sample of size n from the following pdf f (x; 0) = 020-'[(00. a) Find the distribution of Y = - In X1 (suggestion: use the Jacobian method). (b) Find a function of T = - En, In(Xi) that is a pivotal quantity and construct a two-sided (1 - a) confidence interval for 0. ( c ) Suppose you would like to test Ho : 0 = 00 versus Ha : 0 = 01(r