Run-time exception is called unchecked exception since it's not checked during compile time. Everything under throwable except ERROR and RuntimeException are checked exception. Adding Runtime exception in program will decrease the clarity of program.

Is RuntimeException a checked exception or unchecked?

It is up to the programmers to be civilized, and specify or catch the exceptions. In Java exceptions under Error and RuntimeException classes are unchecked exceptions, everything else under throwable is checked.

Is ArrayIndexOutofBoundsException checked or unchecked?

ArrayIndexOutofBoundsException is an unchecked exception. Therefore, the java compiler will not check if a given block of code throws it.