Do I have to claim rental income when family member pays rent below fair market rate?

We just purchase a second home.  My father lives there and pays me a monthly rent which is below fair market rate.   He pays for the utilities.  I pay for home owner insurance and property tax.  Do I have to claim his rent money as a rental income?  If I do, can I also claim home owner insurance and property tax as rental expense?

I am filing for the standard deduction.  Thanks.