[This article was first published on

Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.

**R – Xi'an's Og**, 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.

**T**he weekend riddle from The Riddler is rather straightforward [my wording and simplification]:

Construct a decimal number X between 0 and 1 by drawing the first digit a¹ uniformly over {0,1,…,9}, the second digit a² uniformly over {0,1,…,9}, &tc., until 0 is attained. What is the expectation of this random variable X?

Since each new digit has expectation half of the previous digit, the expectation is an infinite geometric series with common ratio 20⁻¹ and factor 9, leading to an expectation of 9/19. As verified with the following R code:

skr<-function(){ a=9;b=0 while((a<-sample(rep(0:a,2),1))>0)b=10*b+a while(b>=1)b=b/10 return(b)}

To

**leave a comment**for the author, please follow the link and comment on their blog:**R – Xi'an's Og**.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.