Probability distribution of k consecutive successes with n maximum trials

The name of the pictureThe name of the pictureThe name of the pictureClash Royale CLAN TAG#URR8PPP











up vote
1
down vote

favorite












Let $X$ be a random variable that represents the number of trials of a given experiment. The outcome of a single trial is a Bernoulli random variable, with probability of success $p$, and trials are independent.



The maximum number of trials is $n$, but if there are $k<n$ consecutive successes the experiment ends.



What is the probability distribution?







share|cite|improve this question
























    up vote
    1
    down vote

    favorite












    Let $X$ be a random variable that represents the number of trials of a given experiment. The outcome of a single trial is a Bernoulli random variable, with probability of success $p$, and trials are independent.



    The maximum number of trials is $n$, but if there are $k<n$ consecutive successes the experiment ends.



    What is the probability distribution?







    share|cite|improve this question






















      up vote
      1
      down vote

      favorite









      up vote
      1
      down vote

      favorite











      Let $X$ be a random variable that represents the number of trials of a given experiment. The outcome of a single trial is a Bernoulli random variable, with probability of success $p$, and trials are independent.



      The maximum number of trials is $n$, but if there are $k<n$ consecutive successes the experiment ends.



      What is the probability distribution?







      share|cite|improve this question












      Let $X$ be a random variable that represents the number of trials of a given experiment. The outcome of a single trial is a Bernoulli random variable, with probability of success $p$, and trials are independent.



      The maximum number of trials is $n$, but if there are $k<n$ consecutive successes the experiment ends.



      What is the probability distribution?









      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked Aug 17 '14 at 16:54









      vladimirm

      605514




      605514




















          1 Answer
          1






          active

          oldest

          votes

















          up vote
          0
          down vote













          Let $a_n$ be the required probability.



          Then $a_n+1 = a_n+(1-a_n-k)p^k(1-p)$



          Where $a_0=a_1=a_2=...=a_k-1=0,a_k=p^k$






          share|cite|improve this answer






















            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',
            convertImagesToLinks: true,
            noModals: false,
            showLowRepImageUploadWarning: true,
            reputationToPostImages: 10,
            bindNavPrevention: true,
            postfix: "",
            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%2f901206%2fprobability-distribution-of-k-consecutive-successes-with-n-maximum-trials%23new-answer', 'question_page');

            );

            Post as a guest






























            1 Answer
            1






            active

            oldest

            votes








            1 Answer
            1






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes








            up vote
            0
            down vote













            Let $a_n$ be the required probability.



            Then $a_n+1 = a_n+(1-a_n-k)p^k(1-p)$



            Where $a_0=a_1=a_2=...=a_k-1=0,a_k=p^k$






            share|cite|improve this answer


























              up vote
              0
              down vote













              Let $a_n$ be the required probability.



              Then $a_n+1 = a_n+(1-a_n-k)p^k(1-p)$



              Where $a_0=a_1=a_2=...=a_k-1=0,a_k=p^k$






              share|cite|improve this answer
























                up vote
                0
                down vote










                up vote
                0
                down vote









                Let $a_n$ be the required probability.



                Then $a_n+1 = a_n+(1-a_n-k)p^k(1-p)$



                Where $a_0=a_1=a_2=...=a_k-1=0,a_k=p^k$






                share|cite|improve this answer














                Let $a_n$ be the required probability.



                Then $a_n+1 = a_n+(1-a_n-k)p^k(1-p)$



                Where $a_0=a_1=a_2=...=a_k-1=0,a_k=p^k$







                share|cite|improve this answer














                share|cite|improve this answer



                share|cite|improve this answer








                edited Aug 17 at 8:25

























                answered Jul 17 at 4:46









                Makar

                566116




                566116






















                     

                    draft saved


                    draft discarded


























                     


                    draft saved


                    draft discarded














                    StackExchange.ready(
                    function ()
                    StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f901206%2fprobability-distribution-of-k-consecutive-successes-with-n-maximum-trials%23new-answer', 'question_page');

                    );

                    Post as a guest













































































                    這個網誌中的熱門文章

                    How to combine Bézier curves to a surface?

                    Why am i infinitely getting the same tweet with the Twitter Search API?

                    Carbon dioxide