How to get distribution function












0














I have a density function $g(x,y)=4xy mathbb{I}_{[0,1]times[0,1] }(x,y)$. How can I get a distribution function $G(x,y)$?



I found that $G(x,y)= int _{-infty}^x int _{-infty}^y f(u,v) du dv$ where $f(u,v)$ is density function and $G(x,y)$ distribution function. I this right? How can I use it










share|cite|improve this question



























    0














    I have a density function $g(x,y)=4xy mathbb{I}_{[0,1]times[0,1] }(x,y)$. How can I get a distribution function $G(x,y)$?



    I found that $G(x,y)= int _{-infty}^x int _{-infty}^y f(u,v) du dv$ where $f(u,v)$ is density function and $G(x,y)$ distribution function. I this right? How can I use it










    share|cite|improve this question

























      0












      0








      0







      I have a density function $g(x,y)=4xy mathbb{I}_{[0,1]times[0,1] }(x,y)$. How can I get a distribution function $G(x,y)$?



      I found that $G(x,y)= int _{-infty}^x int _{-infty}^y f(u,v) du dv$ where $f(u,v)$ is density function and $G(x,y)$ distribution function. I this right? How can I use it










      share|cite|improve this question













      I have a density function $g(x,y)=4xy mathbb{I}_{[0,1]times[0,1] }(x,y)$. How can I get a distribution function $G(x,y)$?



      I found that $G(x,y)= int _{-infty}^x int _{-infty}^y f(u,v) du dv$ where $f(u,v)$ is density function and $G(x,y)$ distribution function. I this right? How can I use it







      probability integration probability-theory probability-distributions density-function






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked Nov 26 at 9:48









      Atstovas

      697




      697






















          1 Answer
          1






          active

          oldest

          votes


















          1














          $G(x,y)=int_0^{x}int_0^{y} 4uv du dv=x^{2}y^{2}$ for $0leq x,y leq 1$. For $0leq x leq 1$ and $y >1$ we have $G(x,y)=int_0^{x}int_0^{1} 4uv du dv=x^{2}$ and for $0leq y leq 1$ and $x >1$ we have $G(x,y)=y^{2}$. Finally $G(x,y) =1$ if $x,y >1$ and $0$ of $x,y<0$.






          share|cite|improve this answer





















          • Could you explain me why you took those intervals for example if $0geq x, y geq 1$ you took integrals $int_0^x int_0^y$?
            – Atstovas
            Nov 26 at 10:07






          • 1




            Since $g(x,y)=0$ if $x<0$ or $y<0$ all integrals start from $0$. If $x>1$ then the integral from $0$ to $x$ becomes integral from $0$ to $1$ because the density function vanishes for outside $[0,1]$ so it makes no contribution to the integral from $1$ to $x$, etc.
            – Kavi Rama Murthy
            Nov 26 at 10:12











          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%2f3014118%2fhow-to-get-distribution-function%23new-answer', 'question_page');
          }
          );

          Post as a guest















          Required, but never shown

























          1 Answer
          1






          active

          oldest

          votes








          1 Answer
          1






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes









          1














          $G(x,y)=int_0^{x}int_0^{y} 4uv du dv=x^{2}y^{2}$ for $0leq x,y leq 1$. For $0leq x leq 1$ and $y >1$ we have $G(x,y)=int_0^{x}int_0^{1} 4uv du dv=x^{2}$ and for $0leq y leq 1$ and $x >1$ we have $G(x,y)=y^{2}$. Finally $G(x,y) =1$ if $x,y >1$ and $0$ of $x,y<0$.






          share|cite|improve this answer





















          • Could you explain me why you took those intervals for example if $0geq x, y geq 1$ you took integrals $int_0^x int_0^y$?
            – Atstovas
            Nov 26 at 10:07






          • 1




            Since $g(x,y)=0$ if $x<0$ or $y<0$ all integrals start from $0$. If $x>1$ then the integral from $0$ to $x$ becomes integral from $0$ to $1$ because the density function vanishes for outside $[0,1]$ so it makes no contribution to the integral from $1$ to $x$, etc.
            – Kavi Rama Murthy
            Nov 26 at 10:12
















          1














          $G(x,y)=int_0^{x}int_0^{y} 4uv du dv=x^{2}y^{2}$ for $0leq x,y leq 1$. For $0leq x leq 1$ and $y >1$ we have $G(x,y)=int_0^{x}int_0^{1} 4uv du dv=x^{2}$ and for $0leq y leq 1$ and $x >1$ we have $G(x,y)=y^{2}$. Finally $G(x,y) =1$ if $x,y >1$ and $0$ of $x,y<0$.






          share|cite|improve this answer





















          • Could you explain me why you took those intervals for example if $0geq x, y geq 1$ you took integrals $int_0^x int_0^y$?
            – Atstovas
            Nov 26 at 10:07






          • 1




            Since $g(x,y)=0$ if $x<0$ or $y<0$ all integrals start from $0$. If $x>1$ then the integral from $0$ to $x$ becomes integral from $0$ to $1$ because the density function vanishes for outside $[0,1]$ so it makes no contribution to the integral from $1$ to $x$, etc.
            – Kavi Rama Murthy
            Nov 26 at 10:12














          1












          1








          1






          $G(x,y)=int_0^{x}int_0^{y} 4uv du dv=x^{2}y^{2}$ for $0leq x,y leq 1$. For $0leq x leq 1$ and $y >1$ we have $G(x,y)=int_0^{x}int_0^{1} 4uv du dv=x^{2}$ and for $0leq y leq 1$ and $x >1$ we have $G(x,y)=y^{2}$. Finally $G(x,y) =1$ if $x,y >1$ and $0$ of $x,y<0$.






          share|cite|improve this answer












          $G(x,y)=int_0^{x}int_0^{y} 4uv du dv=x^{2}y^{2}$ for $0leq x,y leq 1$. For $0leq x leq 1$ and $y >1$ we have $G(x,y)=int_0^{x}int_0^{1} 4uv du dv=x^{2}$ and for $0leq y leq 1$ and $x >1$ we have $G(x,y)=y^{2}$. Finally $G(x,y) =1$ if $x,y >1$ and $0$ of $x,y<0$.







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered Nov 26 at 9:54









          Kavi Rama Murthy

          49.1k31854




          49.1k31854












          • Could you explain me why you took those intervals for example if $0geq x, y geq 1$ you took integrals $int_0^x int_0^y$?
            – Atstovas
            Nov 26 at 10:07






          • 1




            Since $g(x,y)=0$ if $x<0$ or $y<0$ all integrals start from $0$. If $x>1$ then the integral from $0$ to $x$ becomes integral from $0$ to $1$ because the density function vanishes for outside $[0,1]$ so it makes no contribution to the integral from $1$ to $x$, etc.
            – Kavi Rama Murthy
            Nov 26 at 10:12


















          • Could you explain me why you took those intervals for example if $0geq x, y geq 1$ you took integrals $int_0^x int_0^y$?
            – Atstovas
            Nov 26 at 10:07






          • 1




            Since $g(x,y)=0$ if $x<0$ or $y<0$ all integrals start from $0$. If $x>1$ then the integral from $0$ to $x$ becomes integral from $0$ to $1$ because the density function vanishes for outside $[0,1]$ so it makes no contribution to the integral from $1$ to $x$, etc.
            – Kavi Rama Murthy
            Nov 26 at 10:12
















          Could you explain me why you took those intervals for example if $0geq x, y geq 1$ you took integrals $int_0^x int_0^y$?
          – Atstovas
          Nov 26 at 10:07




          Could you explain me why you took those intervals for example if $0geq x, y geq 1$ you took integrals $int_0^x int_0^y$?
          – Atstovas
          Nov 26 at 10:07




          1




          1




          Since $g(x,y)=0$ if $x<0$ or $y<0$ all integrals start from $0$. If $x>1$ then the integral from $0$ to $x$ becomes integral from $0$ to $1$ because the density function vanishes for outside $[0,1]$ so it makes no contribution to the integral from $1$ to $x$, etc.
          – Kavi Rama Murthy
          Nov 26 at 10:12




          Since $g(x,y)=0$ if $x<0$ or $y<0$ all integrals start from $0$. If $x>1$ then the integral from $0$ to $x$ becomes integral from $0$ to $1$ because the density function vanishes for outside $[0,1]$ so it makes no contribution to the integral from $1$ to $x$, etc.
          – Kavi Rama Murthy
          Nov 26 at 10:12


















          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%2f3014118%2fhow-to-get-distribution-function%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

          Probability when a professor distributes a quiz and homework assignment to a class of n students.

          Aardman Animations

          Are they similar matrix