2. Consider a random sample X1. ..., N'a with density where # 3 01. [a) Show that - log X, follows the exponential distribution with mean 1/8. (5 marks] (b) Show that -20 2 log N, follows the chi-square distribution. Derive the degrees of freedom of the distribution. 15 marks] (c) Derive a (1 - a) confidence interval for 4. 17 marks] (d) Assume & Bayesian paradigm, and set the prior density of 8 to be riff) - be " for # 3 0. Derive a (1 - a) credible interval for E(X;). [10 marks]