Question: Statistics: "Variance[f(NormalRandomVariables)]": How does Maple treat the variables? (symbolically)

Hi I'm Oscar and I'm new on this forum.

I would like to know how does Maple manage Normal random variables when I want to obtain a symbolic expresion like the following (use of Variance to compute symbolically the variance of a combination of normal random variables with its characteristic parameters also symbolically defined)

with(Statistics):

x:=RandomVariable(Normal(Mux,Sigmax)):

y:=RandomVariable(Normal(Muy,Sigmay)):

z:=Variance(x^2+y^2+x*y+c): (1)

(that is to say: x and y  - and obviously the output z - are random variables , and c is a constant).

running the code above, Maple 14 gives to me the following result:

2*Sigmay^4+Muy^2*Sigmax^2+2*Sigmax^4+4*Sigmax^2*Muy*Mux+4*Sigmax^2*Mux^2+

Sigmay^2*Sigmax^2+4*Sigmay^2*Muy^2+4*Sigmay^2*Muy*Mux+Sigmay^2*Mux^2

However I don't know what assumptions it is doing Maple and what formula it's aplying to calculate that variance. The only thing I know (or I can estimate) is that, in the above example code, is using some kind of approximation (note that I've introduced an expression that is not linear in the random variables*).

*To say this i've made an useful comprobation: i've defined two sequences of normal random numbers in Matlab (x_sequence, y_sequence) and, later, i've obtained the variance of the non-linear combination given by z in (1). The variance (2) given by Maple (substiting each one of each one of the distribution parameters) is similar, but not exact, to the calculated by Matlab one.

To sum up: I want to know what formula it is using Maple 14 to compute the Variance of an expresion composed by (non necessarily linear) combinations of random variables (I want the "general" formula)

Thanks in Advance.

I wait for your response.

Óscar