Question: A question about type recognition

Let X₁, ...X_N  names of RandomVariable type and R a random variable defined as a function of  X₁, ...X_N.
(In Maple type(R, RandomVariable) returns false as R doesn't inherit the RandomVariable type.)

Given an expression of R I would like to determine if R is :

• either a linear combination of X₁, ...X_N ,
  example R = a*X₁ + X₂ + 1
  (I know how to handle this situation)
   
• or a linear combination of products of the X₁, ...X_N ,
  example R = a*X₁*X₂ + b*X₃
  (I feel I know how to handle this situation too)
   
• or a linear combination of functions, or products of functions, of  X₁, ...X_N .
  example R = a*f(X₁, X₂) + b*X₃*g(X₄) + c*X₁ + d*X₁*X₂
  (here I've no idea at all)

In the command hastype(R, some_type), how can I construct type some_type in order it returns an answer which matches the reqierements above?

RV_Type.mw

Thanks in advance for any suggestion