# Problem 1
# (a)
# I am goign to genearte a sample of Cauchy distribution with the sample size
# of n = 5 (and subsequently 10, 40 and 200). Calculate the median and store it and
# repeat again many times. The level of prediction interval is obtained as percentiles around
# the midpoint of the collection of median values.
n <- 5
# I am using 100,000 simulated medians.
medians <- matrix(NA,nrow=100000)
for (i in 1:100000) {
medians[i] <- sort( rcauchy(n) )[3]
}
medians <- sort(medians)
line1 <- paste(" 5 ", "[",medians[2500] , ", ",medians[97501], "] [",medians[500],", ",medians[99501],"]")
line1 <- paste(line1, " [", medians[50], ", ",medians[99951],"]")
n <- 10
for (i in 1:100000) {
medians[i] <- sort( rcauchy(n) )[5]
}
medians <- sort(medians)
line2 <- paste(" 10 ", "[",medians[2500] , ", ",medians[97501], "] [",medians[500],", ",medians[99501],"]")
line2 <- paste(line2, " [", medians[50], ", ",medians[99951],"]")
n <- 40
for (i in 1:100000) {
medians[i] <- sort( rcauchy(n) )[20]
}
medians <- sort(medians)
line3 <- paste(" 40 ", "[",medians[2500] , ", ",medians[97501], "] [",medians[500],", ",medians[99501],"]")
line3 <- paste(line3, " [", medians[50], ", ",medians[99951],"]")
n <- 200

Choose any published database from the internet such as the Census...