A Little Sampling Puzzle

[This article was first published on mickeymousemodels, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)
Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.

Suppose you have 10 objects from which you take a sample of size 20 (with replacement, or you’re in trouble). What’s the probability that each object was chosen at least once? Getting an answer via simulation is pleasantly easy:

f <- function(n=10, k=20) {
  x <- 1:n
  x.sample <- sample(x, size=k, replace=TRUE)
  return(length(unique(x.sample)) == n)
}

num.simulations <- 100000
table(replicate(num.simulations, f())) / num.simulations

You should see a number close to 0.215, which is confirmed by the analytic solution:

g 

The second term is the probability that at least one object was not sampled. Enjoy!

To leave a comment for the author, please follow the link and comment on their blog: mickeymousemodels.

R-bloggers.com offers daily e-mail updates about R news and tutorials about learning R and many other topics. Click here if you're looking to post or find an R/data-science job.
Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.

Never miss an update!
Subscribe to R-bloggers to receive
e-mails with the latest R posts.
(You will not see this message again.)

Click here to close (This popup will not appear again)