Counterexample for $E[X|Y]=E[X]$ implies $X$ and $Y$ independent
1
$begingroup$
Statement: $E[X|Y]=E[X]$ implies $X$ and $Y$ independent.
I quite sure that it's not true, And I trying to find an Counterexample for this. but it's hard for me to find one.
probability conditional-expectation
asked Dec 14 '18 at 11:57
Mr.OYMr.OY
16610
$endgroup$
add a comment |
1
$begingroup$
Statement: $E[X|Y]=E[X]$ implies $X$ and $Y$ independent.
I quite sure that it's not true, And I trying to find an Counterexample for this. but it's hard for me to find one.
probability conditional-expectation
asked Dec 14 '18 at 11:57
Mr.OYMr.OY
16610
$endgroup$
2
$begingroup$
See the following post: Is there any counterexample to show that $X,Y$ are two random variables and $E(Xmid Y)=E(X)$, but $X$ and $Y$ are not independent.
$endgroup$
– projectilemotion
Dec 14 '18 at 12:01
$begingroup$
I didn't found it before. Thank you
$endgroup$
– Mr.OY
Dec 14 '18 at 12:24
$begingroup$
After three rather basic questions about conditional expectations in the measure theory sense of the term... Do you have any textbook on the subject at your disposal? Otherwise, I can already predict the long string of elementary questions you are susceptible to ask about it...
$endgroup$
– Did
Dec 14 '18 at 12:39
$begingroup$
@Did I got one, but it seems not to have everything in it, and there are some that points that are not clear, and of course there are questions which I need to figure, such as this one. about those 3 questions, expect for the second one none of them seems to me basic.
$endgroup$
– Mr.OY
Dec 14 '18 at 12:51
$begingroup$
The present one is explained in every decent source on the subject.
$endgroup$
– Did
Dec 14 '18 at 13:57
add a comment |
1
1
1
$begingroup$
Statement: $E[X|Y]=E[X]$ implies $X$ and $Y$ independent.
I quite sure that it's not true, And I trying to find an Counterexample for this. but it's hard for me to find one.
probability conditional-expectation
asked Dec 14 '18 at 11:57
Mr.OYMr.OY
16610
$endgroup$
Statement: $E[X|Y]=E[X]$ implies $X$ and $Y$ independent.
I quite sure that it's not true, And I trying to find an Counterexample for this. but it's hard for me to find one.
probability conditional-expectation
probability conditional-expectation
asked Dec 14 '18 at 11:57
Mr.OYMr.OY
16610
asked Dec 14 '18 at 11:57
Mr.OYMr.OY
16610
asked Dec 14 '18 at 11:57
Mr.OYMr.OY
16610
asked Dec 14 '18 at 11:57
Mr.OYMr.OY
16610
asked Dec 14 '18 at 11:57
Mr.OYMr.OY
16610
16610
2
$begingroup$
See the following post: Is there any counterexample to show that $X,Y$ are two random variables and $E(Xmid Y)=E(X)$, but $X$ and $Y$ are not independent.
$endgroup$
– projectilemotion
Dec 14 '18 at 12:01
$begingroup$
I didn't found it before. Thank you
$endgroup$
– Mr.OY
Dec 14 '18 at 12:24
$begingroup$
After three rather basic questions about conditional expectations in the measure theory sense of the term... Do you have any textbook on the subject at your disposal? Otherwise, I can already predict the long string of elementary questions you are susceptible to ask about it...
$endgroup$
– Did
Dec 14 '18 at 12:39
$begingroup$
@Did I got one, but it seems not to have everything in it, and there are some that points that are not clear, and of course there are questions which I need to figure, such as this one. about those 3 questions, expect for the second one none of them seems to me basic.
$endgroup$
– Mr.OY
Dec 14 '18 at 12:51
$begingroup$
The present one is explained in every decent source on the subject.
$endgroup$
– Did
Dec 14 '18 at 13:57
add a comment |
2
$begingroup$
See the following post: Is there any counterexample to show that $X,Y$ are two random variables and $E(Xmid Y)=E(X)$, but $X$ and $Y$ are not independent.
$endgroup$
– projectilemotion
Dec 14 '18 at 12:01
$begingroup$
I didn't found it before. Thank you
$endgroup$
– Mr.OY
Dec 14 '18 at 12:24
$begingroup$
After three rather basic questions about conditional expectations in the measure theory sense of the term... Do you have any textbook on the subject at your disposal? Otherwise, I can already predict the long string of elementary questions you are susceptible to ask about it...
$endgroup$
– Did
Dec 14 '18 at 12:39
$begingroup$
@Did I got one, but it seems not to have everything in it, and there are some that points that are not clear, and of course there are questions which I need to figure, such as this one. about those 3 questions, expect for the second one none of them seems to me basic.
$endgroup$
– Mr.OY
Dec 14 '18 at 12:51
$begingroup$
The present one is explained in every decent source on the subject.
$endgroup$
– Did
Dec 14 '18 at 13:57
2
2
$begingroup$
See the following post: Is there any counterexample to show that $X,Y$ are two random variables and $E(Xmid Y)=E(X)$, but $X$ and $Y$ are not independent.
$endgroup$
– projectilemotion
Dec 14 '18 at 12:01
$begingroup$
See the following post: Is there any counterexample to show that $X,Y$ are two random variables and $E(Xmid Y)=E(X)$, but $X$ and $Y$ are not independent.
$endgroup$
– projectilemotion
Dec 14 '18 at 12:01
$begingroup$
I didn't found it before. Thank you
$endgroup$
– Mr.OY
Dec 14 '18 at 12:24
$begingroup$
I didn't found it before. Thank you
$endgroup$
– Mr.OY
Dec 14 '18 at 12:24
$begingroup$
After three rather basic questions about conditional expectations in the measure theory sense of the term... Do you have any textbook on the subject at your disposal? Otherwise, I can already predict the long string of elementary questions you are susceptible to ask about it...
$endgroup$
– Did
Dec 14 '18 at 12:39
$begingroup$
After three rather basic questions about conditional expectations in the measure theory sense of the term... Do you have any textbook on the subject at your disposal? Otherwise, I can already predict the long string of elementary questions you are susceptible to ask about it...
$endgroup$
– Did
Dec 14 '18 at 12:39
$begingroup$
@Did I got one, but it seems not to have everything in it, and there are some that points that are not clear, and of course there are questions which I need to figure, such as this one. about those 3 questions, expect for the second one none of them seems to me basic.
$endgroup$
– Mr.OY
Dec 14 '18 at 12:51
$begingroup$
@Did I got one, but it seems not to have everything in it, and there are some that points that are not clear, and of course there are questions which I need to figure, such as this one. about those 3 questions, expect for the second one none of them seems to me basic.
$endgroup$
– Mr.OY
Dec 14 '18 at 12:51
$begingroup$
The present one is explained in every decent source on the subject.
$endgroup$
– Did
Dec 14 '18 at 13:57
$begingroup$
The present one is explained in every decent source on the subject.
$endgroup$
– Did
Dec 14 '18 at 13:57
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
});
}
});
draft saved
draft discarded
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%2f3039272%2fcounterexample-for-exy-ex-implies-x-and-y-independent%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
draft saved
draft discarded
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.
draft saved
draft discarded
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%2f3039272%2fcounterexample-for-exy-ex-implies-x-and-y-independent%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
2
$begingroup$
See the following post: Is there any counterexample to show that $X,Y$ are two random variables and $E(Xmid Y)=E(X)$, but $X$ and $Y$ are not independent.
$endgroup$
– projectilemotion
Dec 14 '18 at 12:01
$begingroup$
I didn't found it before. Thank you
$endgroup$
– Mr.OY
Dec 14 '18 at 12:24
$begingroup$
After three rather basic questions about conditional expectations in the measure theory sense of the term... Do you have any textbook on the subject at your disposal? Otherwise, I can already predict the long string of elementary questions you are susceptible to ask about it...
$endgroup$
– Did
Dec 14 '18 at 12:39
$begingroup$
@Did I got one, but it seems not to have everything in it, and there are some that points that are not clear, and of course there are questions which I need to figure, such as this one. about those 3 questions, expect for the second one none of them seems to me basic.
$endgroup$
– Mr.OY
Dec 14 '18 at 12:51
$begingroup$
The present one is explained in every decent source on the subject.
$endgroup$
– Did
Dec 14 '18 at 13:57