ans = matrix(0,4,4, 
	dimnames = list(c("\'TRUTH\'", "CLT", "boot.norm", "boot.quant"),
			    c("mean", "se", "L", "U")))

## generate 50 observations from exponential distribution ##
n = 50
data = rexp(n)
hist(data)


## use law of large numbers to find 'true' population ##
sample.truth = matrix(0,6000)
for (i in 1:length(sample.truth)) {
	sample.truth[i] = mean(rexp(n))
}
ans[1,1] = mean(sample.truth)
ans[1,2] = sd(sample.truth)
ans[1,3] = quantile(sample.truth, .025)
ans[1,4] = quantile(sample.truth, .0975)


## construct classical Z confidence interval, using CLT ##
ans[2,1] = mean(data)
ans[2,2] = sd(data) / sqrt(n)
ans[2,3] = ans[2,1] - qnorm(.975)*ans[2,2]
ans[2,4] = ans[2,1] + qnorm(.975)*ans[2,2]


## obtain 1000 bootstrap samples ##
B = 1000
sample.boot = matrix(0, B)
for (i in 1:B) {
	sample.boot[i] = mean(sample(data, replace=TRUE))
}


## use bootstrap standard error for CI ### 
ans[3,1] = mean(sample.boot);   
ans[3,2] = sd(sample.boot)
ans[3,3] = ans[3,1] - qnorm(.975)*ans[3,2]
ans[3,4] = ans[3,1] + qnorm(.975)*ans[3,2]

## use bootstrap quantiles for CI ##
ans[4,1] = mean(sample.boot)               ## not used for CI
ans[4,2] = sd(sample.boot)                 ## not used for CI
ans[4,3] = quantile(sample.boot, .025)
ans[4,4] = quantile(sample.boot, .975)