Random Quote in java
The using of a public field should be avoided and instead you should use a method to get the value.  

If you take into account that the class will be extended (like written in the problem statement), I would suggest that you add a getRandomQuote() method to the Quote class.  

Also you should make your String array QUOTES private. I don't know what the conventions for the array braces [] are , but I would write it private static final String[] QUOTES  

A Random should be created once and then used as often one needs.So I would suggest to create it at the constructor.  

private Random random;
public Quotes(){
    random = new Random();
} 

public String getRandomQuote(){
// return your random quote here

}  


You should always name your variables and methods in a meaningful easily readable way. So I have renamed rand to random.