Minimum expected value over all probability functions
$begingroup$
Find the minimum value of $E[X]$ over all probability density functions f(x) satisfying the following three constraints:
(I) $f(x) = 0 $ for $x leq 0$
(II) $ int_{-infty}^{infty} f(x) dx = 1 $
(III) $h(f) = h$
Thanks!
probability variational-analysis
asked Dec 3 '18 at 20:16
FelipeFelipe
1108
$endgroup$
add a comment |
$begingroup$
Find the minimum value of $E[X]$ over all probability density functions f(x) satisfying the following three constraints:
(I) $f(x) = 0 $ for $x leq 0$
(II) $ int_{-infty}^{infty} f(x) dx = 1 $
(III) $h(f) = h$
Thanks!
probability variational-analysis
asked Dec 3 '18 at 20:16
FelipeFelipe
1108
$endgroup$
$begingroup$
Can you elaborate what's $h(f)$ and $h$?
$endgroup$
– Todor Markov
Dec 3 '18 at 20:24
$begingroup$
That is the problem 22 of chapter 12 from Tomas cover information Theory. I think it's a functional
$endgroup$
– Felipe
Dec 3 '18 at 20:48
add a comment |
$begingroup$
Find the minimum value of $E[X]$ over all probability density functions f(x) satisfying the following three constraints:
(I) $f(x) = 0 $ for $x leq 0$
(II) $ int_{-infty}^{infty} f(x) dx = 1 $
(III) $h(f) = h$
Thanks!
probability variational-analysis
asked Dec 3 '18 at 20:16
FelipeFelipe
1108
$endgroup$
Find the minimum value of $E[X]$ over all probability density functions f(x) satisfying the following three constraints:
(I) $f(x) = 0 $ for $x leq 0$
(II) $ int_{-infty}^{infty} f(x) dx = 1 $
(III) $h(f) = h$
Thanks!
probability variational-analysis
probability variational-analysis
asked Dec 3 '18 at 20:16
FelipeFelipe
1108
asked Dec 3 '18 at 20:16
FelipeFelipe
1108
asked Dec 3 '18 at 20:16
FelipeFelipe
1108
asked Dec 3 '18 at 20:16
FelipeFelipe
1108
asked Dec 3 '18 at 20:16
FelipeFelipe
1108
1108
$begingroup$
Can you elaborate what's $h(f)$ and $h$?
$endgroup$
– Todor Markov
Dec 3 '18 at 20:24
$begingroup$
That is the problem 22 of chapter 12 from Tomas cover information Theory. I think it's a functional
$endgroup$
– Felipe
Dec 3 '18 at 20:48
add a comment |
$begingroup$
Can you elaborate what's $h(f)$ and $h$?
$endgroup$
– Todor Markov
Dec 3 '18 at 20:24
$begingroup$
That is the problem 22 of chapter 12 from Tomas cover information Theory. I think it's a functional
$endgroup$
– Felipe
Dec 3 '18 at 20:48
$begingroup$
Can you elaborate what's $h(f)$ and $h$?
$endgroup$
– Todor Markov
Dec 3 '18 at 20:24
$begingroup$
Can you elaborate what's $h(f)$ and $h$?
$endgroup$
– Todor Markov
Dec 3 '18 at 20:24
$begingroup$
That is the problem 22 of chapter 12 from Tomas cover information Theory. I think it's a functional
$endgroup$
– Felipe
Dec 3 '18 at 20:48
$begingroup$
That is the problem 22 of chapter 12 from Tomas cover information Theory. I think it's a functional
$endgroup$
– Felipe
Dec 3 '18 at 20:48
add a comment |
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$begingroup$
Can you elaborate what's $h(f)$ and $h$?
$endgroup$
– Todor Markov
Dec 3 '18 at 20:24
$begingroup$
That is the problem 22 of chapter 12 from Tomas cover information Theory. I think it's a functional
$endgroup$
– Felipe
Dec 3 '18 at 20:48