It's definitely not random. For example there is very little chance it contains a 4, and a very good chance it contains a 1.
4-digit Birthday-pins are probably good as long as they're not your birthday or that of your kids, and you do the last 2 digits of year, last digit of month, last digit of day, go capture as much of the entropy from the date as possible.
On a side note, I remember back in 2004, a colleague born on Feb 29th, 1984 was unable to enter the U.S. H1B renewal website because someone forgot about leap years in their date validation logic.