The constructor of class Calculator must be defined explicitly in order to throw RemoteException. This is necessary because the constructor of its superclass, UnicastRemoteObject, throws it.
Implementations of method add in Client and Proxy are public because the access modifier cannot be made more restrictive. All members of interfaces are implicitly public (§6.6.1.).
Methods of interface CalculatorIF must throw RemoteException. If they don't, rmic complains that CalculatorIF is not a valid remote interface when it tries to create Stub and Skel.
Methods of class Proxy do not throw RemoteException, contrary to methods of class Calculator, although they implement methods of interface CalculatorIF that throw RemoteException. This is accepted by the language (§8.4.4).