mean and covariance of a random process












0














I'm looking at an example from a book I'm reading,



How does it formulate the mean?
I am thinking $$E[X[n]] = sumlimits^infty_{-infty} X[n]P[X[n]] =\
sumlimits^infty_{n=-infty} X[n = even] frac{1}{2} + X[n = even] frac{1}{2} + X[n = odd] frac{9}{10} + X[n = odd] frac{1}{10} \
= sumlimits^infty_{-infty} frac{1}{2}-frac{1}{2}+frac{1}{3}frac{9}{10}-3frac{1}{10} = 0$$

Does this formulation look right? I'm confused when X[n] can be probabilistically assigned values.










share|cite|improve this question






















  • What does $X[n]$ mean? Did you mean $X_n$?
    – Will M.
    Nov 19 '18 at 6:08










  • @WillM. Yes, I think that makes it easier to write.
    – drerD
    Nov 19 '18 at 6:10






  • 1




    The formulae you wrote does not make sense to me. $mathbf{E}(X_n)$ is clearly zero for $n$ even and it is $dfrac{1}{3} times dfrac{9}{10} - 3 times dfrac{1}{10} = 0$ for $n$ odd.
    – Will M.
    Nov 19 '18 at 6:13










  • It seems like you are thinking of $X$ as the random variable. That is not correct, $X_n$ is a random variable, $X$ is a "random sequence."
    – Will M.
    Nov 19 '18 at 6:14






  • 1




    Ok, stop using $X[k]$ because that IS confusing. For a random sequence $X$ we can define a function $m_X$ such that $m_X(n) = mathbf{E}(X_n).$
    – Will M.
    Nov 19 '18 at 6:24
















0














I'm looking at an example from a book I'm reading,



How does it formulate the mean?
I am thinking $$E[X[n]] = sumlimits^infty_{-infty} X[n]P[X[n]] =\
sumlimits^infty_{n=-infty} X[n = even] frac{1}{2} + X[n = even] frac{1}{2} + X[n = odd] frac{9}{10} + X[n = odd] frac{1}{10} \
= sumlimits^infty_{-infty} frac{1}{2}-frac{1}{2}+frac{1}{3}frac{9}{10}-3frac{1}{10} = 0$$

Does this formulation look right? I'm confused when X[n] can be probabilistically assigned values.










share|cite|improve this question






















  • What does $X[n]$ mean? Did you mean $X_n$?
    – Will M.
    Nov 19 '18 at 6:08










  • @WillM. Yes, I think that makes it easier to write.
    – drerD
    Nov 19 '18 at 6:10






  • 1




    The formulae you wrote does not make sense to me. $mathbf{E}(X_n)$ is clearly zero for $n$ even and it is $dfrac{1}{3} times dfrac{9}{10} - 3 times dfrac{1}{10} = 0$ for $n$ odd.
    – Will M.
    Nov 19 '18 at 6:13










  • It seems like you are thinking of $X$ as the random variable. That is not correct, $X_n$ is a random variable, $X$ is a "random sequence."
    – Will M.
    Nov 19 '18 at 6:14






  • 1




    Ok, stop using $X[k]$ because that IS confusing. For a random sequence $X$ we can define a function $m_X$ such that $m_X(n) = mathbf{E}(X_n).$
    – Will M.
    Nov 19 '18 at 6:24














0












0








0







I'm looking at an example from a book I'm reading,



How does it formulate the mean?
I am thinking $$E[X[n]] = sumlimits^infty_{-infty} X[n]P[X[n]] =\
sumlimits^infty_{n=-infty} X[n = even] frac{1}{2} + X[n = even] frac{1}{2} + X[n = odd] frac{9}{10} + X[n = odd] frac{1}{10} \
= sumlimits^infty_{-infty} frac{1}{2}-frac{1}{2}+frac{1}{3}frac{9}{10}-3frac{1}{10} = 0$$

Does this formulation look right? I'm confused when X[n] can be probabilistically assigned values.










share|cite|improve this question













I'm looking at an example from a book I'm reading,



How does it formulate the mean?
I am thinking $$E[X[n]] = sumlimits^infty_{-infty} X[n]P[X[n]] =\
sumlimits^infty_{n=-infty} X[n = even] frac{1}{2} + X[n = even] frac{1}{2} + X[n = odd] frac{9}{10} + X[n = odd] frac{1}{10} \
= sumlimits^infty_{-infty} frac{1}{2}-frac{1}{2}+frac{1}{3}frac{9}{10}-3frac{1}{10} = 0$$

Does this formulation look right? I'm confused when X[n] can be probabilistically assigned values.







random-variables random-walk






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Nov 19 '18 at 6:01









drerD

1519




1519












  • What does $X[n]$ mean? Did you mean $X_n$?
    – Will M.
    Nov 19 '18 at 6:08










  • @WillM. Yes, I think that makes it easier to write.
    – drerD
    Nov 19 '18 at 6:10






  • 1




    The formulae you wrote does not make sense to me. $mathbf{E}(X_n)$ is clearly zero for $n$ even and it is $dfrac{1}{3} times dfrac{9}{10} - 3 times dfrac{1}{10} = 0$ for $n$ odd.
    – Will M.
    Nov 19 '18 at 6:13










  • It seems like you are thinking of $X$ as the random variable. That is not correct, $X_n$ is a random variable, $X$ is a "random sequence."
    – Will M.
    Nov 19 '18 at 6:14






  • 1




    Ok, stop using $X[k]$ because that IS confusing. For a random sequence $X$ we can define a function $m_X$ such that $m_X(n) = mathbf{E}(X_n).$
    – Will M.
    Nov 19 '18 at 6:24


















  • What does $X[n]$ mean? Did you mean $X_n$?
    – Will M.
    Nov 19 '18 at 6:08










  • @WillM. Yes, I think that makes it easier to write.
    – drerD
    Nov 19 '18 at 6:10






  • 1




    The formulae you wrote does not make sense to me. $mathbf{E}(X_n)$ is clearly zero for $n$ even and it is $dfrac{1}{3} times dfrac{9}{10} - 3 times dfrac{1}{10} = 0$ for $n$ odd.
    – Will M.
    Nov 19 '18 at 6:13










  • It seems like you are thinking of $X$ as the random variable. That is not correct, $X_n$ is a random variable, $X$ is a "random sequence."
    – Will M.
    Nov 19 '18 at 6:14






  • 1




    Ok, stop using $X[k]$ because that IS confusing. For a random sequence $X$ we can define a function $m_X$ such that $m_X(n) = mathbf{E}(X_n).$
    – Will M.
    Nov 19 '18 at 6:24
















What does $X[n]$ mean? Did you mean $X_n$?
– Will M.
Nov 19 '18 at 6:08




What does $X[n]$ mean? Did you mean $X_n$?
– Will M.
Nov 19 '18 at 6:08












@WillM. Yes, I think that makes it easier to write.
– drerD
Nov 19 '18 at 6:10




@WillM. Yes, I think that makes it easier to write.
– drerD
Nov 19 '18 at 6:10




1




1




The formulae you wrote does not make sense to me. $mathbf{E}(X_n)$ is clearly zero for $n$ even and it is $dfrac{1}{3} times dfrac{9}{10} - 3 times dfrac{1}{10} = 0$ for $n$ odd.
– Will M.
Nov 19 '18 at 6:13




The formulae you wrote does not make sense to me. $mathbf{E}(X_n)$ is clearly zero for $n$ even and it is $dfrac{1}{3} times dfrac{9}{10} - 3 times dfrac{1}{10} = 0$ for $n$ odd.
– Will M.
Nov 19 '18 at 6:13












It seems like you are thinking of $X$ as the random variable. That is not correct, $X_n$ is a random variable, $X$ is a "random sequence."
– Will M.
Nov 19 '18 at 6:14




It seems like you are thinking of $X$ as the random variable. That is not correct, $X_n$ is a random variable, $X$ is a "random sequence."
– Will M.
Nov 19 '18 at 6:14




1




1




Ok, stop using $X[k]$ because that IS confusing. For a random sequence $X$ we can define a function $m_X$ such that $m_X(n) = mathbf{E}(X_n).$
– Will M.
Nov 19 '18 at 6:24




Ok, stop using $X[k]$ because that IS confusing. For a random sequence $X$ we can define a function $m_X$ such that $m_X(n) = mathbf{E}(X_n).$
– Will M.
Nov 19 '18 at 6:24















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


















StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3004578%2fmean-and-covariance-of-a-random-process%23new-answer', 'question_page');
}
);

Post as a guest















Required, but never shown






























active

oldest

votes













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.





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.




draft saved


draft discarded














StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3004578%2fmean-and-covariance-of-a-random-process%23new-answer', 'question_page');
}
);

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







Popular posts from this blog

AnyDesk - Fatal Program Failure

How to calibrate 16:9 built-in touch-screen to a 4:3 resolution?

QoS: MAC-Priority for clients behind a repeater