Question 2: Precedence and context free grammars [6]

Suppose we have the following set of context free grammar rules, where non-terminals begin with an uppercase letter and terminals are shown in double-quotes: 

 Program --> "begin", Statement, "end"  
 Statement --> Variable, ":=", Expression  
 Expression --> Expression, "#", SubExpr  
 Expression --> Value  
 SubExpr --> SubExpr, "$", Value  
 SubExpr --> SubExpr, "?", Value  
 Value --> Variable  
 Value --> QuadInt  

 Variable --> "w"  
 Variable --> "x"  
 Variable --> "y"  
 Variable --> "z"  
 QuadInt --> "0"  
 QuadInt --> "1"  
 QuadInt --> "2"  
 QuadInt --> "3"  

Sketch the parse tree for the following program, and explain what the precedence and associativity rules for the #, $, and ? operators must be. 

 begin x := 3 $ x # y ? z $ 2 end