No, Randy Jackson and Michael Jackson are not related.
No they are not related.
They aren't related at all. Although Michael does have a brother nicknamed "Randy"
His name is Phil LaMarr. He's also in Pulp Fiction, and does voice-over work for Family Guy and Futurama.
The Randy Jackson of American Idol isn't related to him, but he does have a younger brother called Steven Randall "Randy" Jackson.