Minimum expected value over all probability functions
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
Felipe
798
add a comment |
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
Felipe
798
Can you elaborate what's $h(f)$ and $h$?
– Todor Markov
Dec 3 '18 at 20:24
That is the problem 22 of chapter 12 from Tomas cover information Theory. I think it's a functional
– Felipe
Dec 3 '18 at 20:48
add a comment |
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
Felipe
798
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
Felipe
798
asked Dec 3 '18 at 20:16
Felipe
798
asked Dec 3 '18 at 20:16
Felipe
798
asked Dec 3 '18 at 20:16
Felipe
798
asked Dec 3 '18 at 20:16
Felipe
798
798
Can you elaborate what's $h(f)$ and $h$?
– Todor Markov
Dec 3 '18 at 20:24
That is the problem 22 of chapter 12 from Tomas cover information Theory. I think it's a functional
– Felipe
Dec 3 '18 at 20:48
add a comment |
Can you elaborate what's $h(f)$ and $h$?
– Todor Markov
Dec 3 '18 at 20:24
That is the problem 22 of chapter 12 from Tomas cover information Theory. I think it's a functional
– Felipe
Dec 3 '18 at 20:48
Can you elaborate what's $h(f)$ and $h$?
– Todor Markov
Dec 3 '18 at 20:24
Can you elaborate what's $h(f)$ and $h$?
– Todor Markov
Dec 3 '18 at 20:24
That is the problem 22 of chapter 12 from Tomas cover information Theory. I think it's a functional
– Felipe
Dec 3 '18 at 20:48
That is the problem 22 of chapter 12 from Tomas cover information Theory. I think it's a functional
– Felipe
Dec 3 '18 at 20:48
add a comment |
0
active
oldest
votes
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3024601%2fminimum-expected-value-over-all-probability-functions%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3024601%2fminimum-expected-value-over-all-probability-functions%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Can you elaborate what's $h(f)$ and $h$?
– Todor Markov
Dec 3 '18 at 20:24
That is the problem 22 of chapter 12 from Tomas cover information Theory. I think it's a functional
– Felipe
Dec 3 '18 at 20:48