Below is an example of installing under root mode:
#yum -y install mysql-server
Installed: mysql-server.i386 0:4.1.20-1.RHEL4.1
Dependency Installed: mysql.i386 0:4.1.20-1.RHEL4.1 perl-DBD-MySQL.i386 0:2.9004-3.1 perl-DBI.i386 0:1.40-8
Complete!
After installation, the password is empty. You can log in using: mysql -uroot -p .