Mathematical expectation

*To*: mathgroup at smc.vnet.net*Subject*: [mg84113] Mathematical expectation*From*: Benoît Frénay <benoit.frenay at uclouvain.be>*Date*: Mon, 10 Dec 2007 20:40:00 -0500 (EST)

Hello, I'm new to Mathematica and I'm trying to define a generic mathematical expectation operator (called Esp) for i.i.d variables X[i] following the same distribution as the variable X (i.e. Esp[X[i]] == Esp[X]). My code is Esp[X[_]] := Esp[X] Esp[X[_]^y_] := Esp[X^y] Esp[Esp[x_]] := Esp[x] Esp[Esp[x_]^y_] := Esp[x]^y Esp[x_ + y_] := Esp[x] + Esp[y] Esp[x_ y_] := Esp[x] Esp[y] /; FreeQ[x, y] && FreeQ[y, x] Esp[c_] := c /; FreeQ[c, X] Esp[c_ x_] := c Esp[x] /; NumberQ[c] But when I feed >>> In[14]:= Esp[(X[1] + X[2])^2] I obtain >>> Out[14]= Esp[(X[1] + X[2])^2] In fact, I obtain the correct answer only if I ask Mathematica to expand the inner term: In[16]:= Esp[Expand[(X[1] + X[2])^2]] Out[16]= 2 Esp[X]^2 + 2 Esp[X^2] Where am I wrong? Thanks, Benoît Frénay

**Follow-Ups**:**Re: Mathematical expectation***From:*Carl Woll <carlw@wolfram.com>