Crazy Cauchy: The Cauchy distribution (aka a t distribution with one degree of freedom) is outlier prone (extremely heavy tailed). In R, Cauchy random variables can be simulated using rcauchy(). For...

Crazy Cauchy: The Cauchy distribution (aka a t distribution with one degree of freedom) is outlier prone (extremely heavy tailed). In R, Cauchy random variables can be simulated using rcauchy(). For example, the R code z <->

a. Simulate 50 Cauchy random variables with median 0 and spread 1 and compute a confidence interval for the mean.

b. Simulate 500 Cauchy random variables with median 0 and spread 1 and compute a confidence interval for the mean.

c. Simulate 5000 Cauchy random variables with median 0 and spread 1 and compute a confidence interval for the mean.

d. Simulate 50,000 Cauchy random variables with median 0 and spread 1 and compute a confidence interval for the mean.

e. What might you conclude about the central limit theorem and the Cauchy distribution based on the results in (a)–(d).