The Number of Fixed Points in a Random Permutation

n

2

new sample

distribution

exact

approximate

sample mean: 1.07

standard deviation: 0.999

0

1

2

0.0

0.1

0.2

0.3

0.4

0.5

For a random permutation of

(1,…,n)

, let

X

be the random variable that counts the number of digits that remain in their original position. This Demonstration allows you to compare the relative frequencies of

X

obtained in a sample of size 400 with the exact and approximate distributions of

X

. It also gives the sample mean and standard deviation.