Re: A quick question regarding expectation rules
- To: mathgroup at smc.vnet.net
- Subject: [mg63896] Re: [mg63878] A quick question regarding expectation rules
- From: Bob Hanlon <hanlonr at cox.net>
- Date: Sat, 21 Jan 2006 01:50:42 -0500 (EST)
- Reply-to: hanlonr at cox.net
- Sender: owner-wri-mathgroup at wolfram.com
r={e[1]:>1,
e[x_+y_]:>e[x]+e[y],
e[a_?(NumericQ[#]||AtomQ[#]&&
MemberQ[Attributes[#],Constant]&)*
x_.]:>a*e[x],
e[e[x_]]:>e[x]};
Clear[a,b,x,y];
SetAttributes[{a,b}, Constant]
{e[f[x]],e[a*x],e[b+f[x]],e[3*a+6*e[b*y]]}//.r
{e[f[x]], a*e[x], b + e[f[x]], 3*a + 6*b*e[y]}
Bob Hanlon
>
> From: "Mark Morrissey" <mmorriss at ou.edu>
To: mathgroup at smc.vnet.net
> Subject: [mg63896] [mg63878] A quick question regarding expectation rules
>
>
> Hi Folks - A couple of months ago a lot of you helped me out with
designing
> a set of rules to apply to expectation operator given 'variables' and
> 'constants'. Below is a set of rules that work quite well.
>
>
>
> However, the rules below expect 'x' or any one single default variable. How
> might one go about adjusting these rules so that the variables 'x, y, and z'
> (i.e. multiple variables) can be accounted for?
>
>
>
> For example: E[a x + b y] //. rules[?]= a E[x] + b E[y] ???
>
>
>
> PLEASE note that I'm using a double stuck 'E' in the notebook (not to be
> confused with the exponential function)
>
>
>
> What I have now:
>
>
>
> (* Expectation Rules*)
>
> (* x, y, z, are assumed to be random variables and a, b, c are assumed to
> constants *)
>
> Clear[E,rules];
>
> rules[x_Symbol:x] := {
>
> E[expr_?(FreeQ[#,x]&)] |expr,
>
> E[expr1_?(FreeQ[#,x]&) expr2_?(!FreeQ[#,x]&)]|
>
> expr1 * E[expr2],
>
> E[expr1_?(FreeQ[#,x]&)+expr2_?(!FreeQ[#,x]&)]|expr1+ E[expr2],
> E[E[expr_?(!FreeQ[#,x]&)]]| E[expr]
>
> };
>
>
>
>
>
> In[1]:{E[f[ x]],E[a x], E[b + f[x]], E[a + E[b y]],E[a + E[b y]]} //.
> rules[] (* using the default {rules[x],rules[y]} where 'x' or 'y' are
> assumed to be variables *)
>
>
>
>
>
> Out[1] {E[f[x]],a E[x],b+E[f[x]],a+b y,a+b y}
>
>
>
> Thank you very much.
>
>
>
> Regards - Mark
>
>
>
> Mark Morrissey
>
> Associate Professor, Meteorology
>
> University of Oklahoma
>
> EVAC, 3200 Marshall Ave., Suite 150
>
> Norman, Oklahoma
>
>
>