Consider the variable brain from the Animals data frame in the MASS package.
(a) Estimate with maximum likelihood techniques the mean and variance of brain. Specifically, use the R function fitdistr () with a lognormal distribution.
(b) Suppose that brain is a lognormal variable; then the log of this variable is normal. To check this assertion, plot the cumulative distribution function of brain versus a lognormal cumulative distribution function. In another plot, represent the cumulative distribution function of log-brain versus a normal cumulative distribution function. Is it reasonable to assume that brain follows a lognormal distribution?
(c) Find the mean and standard deviation of brain assuming a lognormal distribution.
(d) Repeat this exercise without the dinosaurs. Comment on the changes in the mean and variance estimates.