[R] Fw: Multiple Integrals

[David Winsemius]

On Aug 30, 2015, at 8:41 AM, Shant Ch via R-help wrote:

> Thank you very much to all for all your responses.
> 
> @Dr. Winsemius, E[f(X)] >=f(E(X)) if f is convex. Now we know |x| is convex function, so clearly in this scenario if we compute the expectation of the ((X1+X2+X3)/3-X4) and then take the absolute, then, we will get a lower bound of the expectation I want to find. 
> 

I understood the error in my thinking when Jeff Newmiller pointed out the minus sign that I had missed.

Thanks;
David.


>      On Saturday, August 29, 2015 7:24 PM, David Winsemius <dwinsemius at comcast.net> wrote:
> 
> 
> 
> On Aug 29, 2015, at 11:35 AM, Shant Ch via R-help wrote:
> 
>> Hello Dr. Berry,
>> 
>> I know the theoretical side but note we are not talking about expectation of sums rather expectation of ABSOLUTE value of the function (X1/3+X2/3+X3/3-X4), i.e. E|X1/3+X2/3+X3/3-X4|  , I don't think this can be handled for log normal distribution by integrals by hand.
>> 
> 
> To Shnant Ch;
> 
> I admit to puzzlement (being a humble country doctor). Can you explain why there should be a difference between the absolute value of an expectation for a sum of values from a function, in this case dlnorm,  that is positive definite versus an expectation simply of the sum of such values?
> 
> -- 
> 
> David Winsemius
> Alameda, CA, USA
> 
> 
> 
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David Winsemius
Alameda, CA, USA