Recently on twitter I saw this idea that if you would pick a number from a uniform distribution [0, 1] and repeat drawing numbers until the sum of the numbers is lager than one, you’ll on average pick e numbers. Didn’t doubt it at all, just thought it would be fun checking this theory (theorem?) in R:

Let’s build a function that can test this. We’ll do it one million times, and then calculate the mean (that should be equal to e).

test_theory <-function(no_tests =10) { results <-vector(mode ="integer", length = no_tests)for(i in1:no_tests) { sum =0 cnt =0while(sum <=1) { sum = sum +runif(1, min =0, max =1) cnt = cnt +1 } results[i] = cnt }return(mean(results))}test_theory(1000000)

[1] 2.719122

e in R is 2.7182818

For a mathematical breakdown [that is beyond my comprehension], see this website.