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What's the relationship of $f$ and $h$ in ${mathbb{E}_i left[ f(g(x,i)) right] = h(mathbb{E}_i left[ g(x,i) right] )}$

0

$begingroup$

Let there be a function $f$ and $h$ satisfying

${mathbb{E}_i left[ f(g(x,i)) right] = h(mathbb{E}_i left[ g(x,i) right] )}$

for an arbitrary 2-variable function $g : mathbb{R}^n times mathbb{R} rightarrow mathbb{R}$,

Is it always possible to find a such a function $h$ for given $f$ ?

integration analysis

share|cite|improve this question

edited Mar 22 at 13:52

Junho

asked Mar 22 at 13:45

JunhoJunho

115

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  please clarify what $x$ and $i$ are.
  $endgroup$
  – Cettt
  Mar 22 at 13:48
  

  
  
  
  

add a comment | 

0

$begingroup$

Let there be a function $f$ and $h$ satisfying

${mathbb{E}_i left[ f(g(x,i)) right] = h(mathbb{E}_i left[ g(x,i) right] )}$

for an arbitrary 2-variable function $g : mathbb{R}^n times mathbb{R} rightarrow mathbb{R}$,

Is it always possible to find a such a function $h$ for given $f$ ?

integration analysis

share|cite|improve this question

edited Mar 22 at 13:52

Junho

asked Mar 22 at 13:45

JunhoJunho

115

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  please clarify what $x$ and $i$ are.
  $endgroup$
  – Cettt
  Mar 22 at 13:48
  

  
  
  
  

add a comment | 

$begingroup$

Let there be a function $f$ and $h$ satisfying

${mathbb{E}_i left[ f(g(x,i)) right] = h(mathbb{E}_i left[ g(x,i) right] )}$

for an arbitrary 2-variable function $g : mathbb{R}^n times mathbb{R} rightarrow mathbb{R}$,

Is it always possible to find a such a function $h$ for given $f$ ?

integration analysis

share|cite|improve this question

edited Mar 22 at 13:52

Junho

asked Mar 22 at 13:45

JunhoJunho

115

$endgroup$

share|cite|improve this question

edited Mar 22 at 13:52

Junho

asked Mar 22 at 13:45

JunhoJunho

115

share|cite|improve this question

edited Mar 22 at 13:52

Junho

asked Mar 22 at 13:45

JunhoJunho

115

asked Mar 22 at 13:45

JunhoJunho

115

asked Mar 22 at 13:45

JunhoJunho

115