Newsflash: [Can] Am I entitled to a partial rent payment between closing date and 1st of next month?

Just bought a property with 2 tenants in it. Am I entitled to the balance of the month’s rent that I own the property? For example:Total rent for January: $2000.00 Take legal ownership (closing date): Jan 22 Rent owed to me = (9 days of ownership/31 total days in January) * $2000.00 = $580Is this right? Or is the previous landlord entitled to the entirety of January’s rent?Thank you