Mixing
Simple Upper Bound for Entropy
$begingroup$
How do we show that:
$-frac{p}{p+n}log_2(frac{p}{p+n})-frac{n}{p+n}log_2(frac{n}{p+n}) leq 1$
I've tried multiplying by p+n and a lot of other stuff, but I can't seem to figure out a simple way of showing this fact (limits of entropy). Thanks in advance for all your help!
limits functions inequality
edited Jan 28 at 12:14
J. W. Tanner
3,9221320
asked Jan 28 at 9:45
James WilsonJames Wilson
83
$endgroup$
add a comment |
$begingroup$
How do we show that:
$-frac{p}{p+n}log_2(frac{p}{p+n})-frac{n}{p+n}log_2(frac{n}{p+n}) leq 1$
I've tried multiplying by p+n and a lot of other stuff, but I can't seem to figure out a simple way of showing this fact (limits of entropy). Thanks in advance for all your help!
limits functions inequality
edited Jan 28 at 12:14
J. W. Tanner
3,9221320
asked Jan 28 at 9:45
James WilsonJames Wilson
83
$endgroup$
$begingroup$
Factor the expression first. What is left ?
$endgroup$
– Claude Leibovici
Jan 28 at 10:35
add a comment |
$begingroup$
How do we show that:
$-frac{p}{p+n}log_2(frac{p}{p+n})-frac{n}{p+n}log_2(frac{n}{p+n}) leq 1$
I've tried multiplying by p+n and a lot of other stuff, but I can't seem to figure out a simple way of showing this fact (limits of entropy). Thanks in advance for all your help!
limits functions inequality
edited Jan 28 at 12:14
J. W. Tanner
3,9221320
asked Jan 28 at 9:45
James WilsonJames Wilson
83
$endgroup$
How do we show that:
$-frac{p}{p+n}log_2(frac{p}{p+n})-frac{n}{p+n}log_2(frac{n}{p+n}) leq 1$
I've tried multiplying by p+n and a lot of other stuff, but I can't seem to figure out a simple way of showing this fact (limits of entropy). Thanks in advance for all your help!
limits functions inequality
limits functions inequality
edited Jan 28 at 12:14
J. W. Tanner
3,9221320
asked Jan 28 at 9:45
James WilsonJames Wilson
83
edited Jan 28 at 12:14
J. W. Tanner
3,9221320
asked Jan 28 at 9:45
James WilsonJames Wilson
83
edited Jan 28 at 12:14
J. W. Tanner
3,9221320
edited Jan 28 at 12:14
J. W. Tanner
3,9221320
edited Jan 28 at 12:14
J. W. Tanner
3,9221320
3,9221320
asked Jan 28 at 9:45
James WilsonJames Wilson
83
asked Jan 28 at 9:45
James WilsonJames Wilson
83
asked Jan 28 at 9:45
James WilsonJames Wilson
83
83
$begingroup$
Factor the expression first. What is left ?
$endgroup$
– Claude Leibovici
Jan 28 at 10:35
add a comment |
$begingroup$
Factor the expression first. What is left ?
$endgroup$
– Claude Leibovici
Jan 28 at 10:35
$begingroup$
Factor the expression first. What is left ?
$endgroup$
– Claude Leibovici
Jan 28 at 10:35
$begingroup$
Factor the expression first. What is left ?
$endgroup$
– Claude Leibovici
Jan 28 at 10:35
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%2f3090667%2fsimple-upper-bound-for-entropy%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.
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%2f3090667%2fsimple-upper-bound-for-entropy%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
$begingroup$
Factor the expression first. What is left ?
$endgroup$
– Claude Leibovici
Jan 28 at 10:35