       Re: Mathematical expectation

• To: mathgroup at smc.vnet.net
• Subject: [mg84137] Re: [mg84113] Mathematical expectation
• From: DrMajorBob <drmajorbob at bigfoot.com>
• Date: Tue, 11 Dec 2007 06:09:24 -0500 (EST)
• References: <2929821.1197341645609.JavaMail.root@m35>

```Add another pattern:

Clear[Esp]
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]
Esp[expr_] /; expr =!= Expand@expr := Esp@Expand@expr

Esp[(X + X)^2]

2 Esp[X]^2 + 2 Esp[X^2]

or, more efficient if Expand could take a lot of time...

Clear[Esp]
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]
Esp[expr_] :=
Module[{expanded = Expand@expr}, Esp@expanded /; expanded =!= expr]

Esp[(X + X)^2]

2 Esp[X]^2 + 2 Esp[X^2]

Bobby

On Mon, 10 Dec 2007 19:40:00 -0600, Benoît Frénay
<benoit.frenay at uclouvain.be> wrote:

> 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:= Esp[(X + X)^2]
> I obtain
>  >>> Out= Esp[(X + X)^2]
> In fact, I obtain the correct answer only if I ask Mathematica to expand
> the inner term:
> In:= Esp[Expand[(X + X)^2]]
> Out= 2 Esp[X]^2 + 2 Esp[X^2]
>
> Where am I wrong?
>
> Thanks,
>
> Benoît Frénay
>
>
>

--
DrMajorBob at bigfoot.com

```

• Prev by Date: Re: From 3D to 2D
• Next by Date: Re: Prefix Forms on the BasicMath Palette
• Previous by thread: Re: Mathematical expectation
• Next by thread: Implementing own data functions