Please solve

3. Time intervals (in minutes) X1, ..., Xn between successive eruptions of a geyser are modeled as Xi ~Exponential(1), where A (> 0) is the eruption rate. We want to report a plausible range for the median inter- val time. The median of the Exponential()) distribution, denoted by 0, equals log 2/1 = 0.693/1. (a) (3 pts) Find the MLE of 1. (b) (3 pts) Find the Fisher information of 1. (c) (3 pts) Construct an approximate 95% confidence interval for A using the asymptotic distri- bution of AMLE. (d) (3 pts) Calculate an approximate 95% confidence interval for the median interval time 0 using the Delta method. Hint: You do not need to derive the Fisher information of 0 from scratch to replace In (0) with In(OMLE) in the bounds of the interval. Just replacing 0 with OMLE in the variance is fine