please solve all parts! Thank you!

2. Multivariate Confidence Intervals from Optim The data in data2 are assumed to come from the following distribution. Xi ~ Lognorm(u,0%), i = 1,2,..., 30 and each Xi is assumed to be independent of all others. The Lognormal distribution can be explored on Wikipedia, and also by typing ?dlognorm into the terminal in R. (a) Use optim to numerically estimate MLEs for both u and o2. (b) Numerically find an approximate 95% confidence interval for the parameter u using optim's esti- mate of the Fisher information. (c) Numerically find an approximate 95% confidence interval for the parameter o2 using optim's estimate of the Fisher information. (d) Now find an approximate 95% confidence interval for V2. You can still use optim's estimate of the Fisher information for 2, but should apply the delta method to obtain a correct confidence interval. = 2. Multivariate Confidence Intervals from Optim The data in data2 are assumed to come from the following distribution. Xi ~ Lognorm(u,0%), i = 1,2,..., 30 and each Xi is assumed to be independent of all others. The Lognormal distribution can be explored on Wikipedia, and also by typing ?dlognorm into the terminal in R. (a) Use optim to numerically estimate MLEs for both u and o2. (b) Numerically find an approximate 95% confidence interval for the parameter u using optim's esti- mate of the Fisher information. (c) Numerically find an approximate 95% confidence interval for the parameter o2 using optim's estimate of the Fisher information. (d) Now find an approximate 95% confidence interval for V2. You can still use optim's estimate of the Fisher information for 2, but should apply the delta method to obtain a correct confidence interval. =