Many banks apparently don't let you choose PINs; however from the limited sample of PINs I know of (mine, my wife, my company and a few others) they're not random; they all have doubled digits (like 2554).
$ pins() { seq -f '%04.0f' 0 9999; }
$ pins | egrep -c '(.)\1'
2710
$ pins | egrep -c '(.).*\1'
4960
$ $ pins |
> sed -r '
> :a; s/^([0-9])(.*)\1/\1\2a/; ta; s/[0-9]/a/
> :b; s/a([0-9])(.*)\1/a\1\2b/; tb; s/[0-9]/b/
> s/([0-9])\1/cc/; s/[0-9]/c/
> s/[0-9]/d/
> ' |
> sort | uniq -c | sort -n
10 aaaa
90 aaab
90 aaba
90 aabb
90 abaa
90 abab
90 abba
90 abbb
720 aabc
720 abac
720 abbc
720 abca
720 abcb
720 abcc
5040 abcd
$