Find the distribution of a variable from joint distribution law

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I'm having trouble with this particular problem.




Let the random vector $(xi, eta)$ has the following joint distribution law
$p(1, 1) = 1/8$, $p(2, 1) = 1/4$, $p(1, 2) = 1/8$, $p(2, 2) = 1/2$.



Find the distribution of $xi$, if $eta = i$, $i = 1, 2$.




What does it mean by the distribution of $xi$? Does this mean that I have to say that




$p(xi, 1) = 1/8 + 1/8 = 1/4$ and $p(xi, 2) = 1/8 + 1/2 = 3/4$




I suspect that it has to do something with joint CDF, but I have no idea how to derive it from the data that I was given.

Any kind of help would be appreciated.




probability probability-distributions




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    up vote
    1
    down vote

    favorite












    I'm having trouble with this particular problem.




    Let the random vector $(xi, eta)$ has the following joint distribution law
    $p(1, 1) = 1/8$, $p(2, 1) = 1/4$, $p(1, 2) = 1/8$, $p(2, 2) = 1/2$.



    Find the distribution of $xi$, if $eta = i$, $i = 1, 2$.




    What does it mean by the distribution of $xi$? Does this mean that I have to say that




    $p(xi, 1) = 1/8 + 1/8 = 1/4$ and $p(xi, 2) = 1/8 + 1/2 = 3/4$




    I suspect that it has to do something with joint CDF, but I have no idea how to derive it from the data that I was given.

    Any kind of help would be appreciated.




    probability probability-distributions




    share|cite|improve this question























      up vote
      1
      down vote

      favorite









      up vote
      1
      down vote

      favorite











      I'm having trouble with this particular problem.




      Let the random vector $(xi, eta)$ has the following joint distribution law
      $p(1, 1) = 1/8$, $p(2, 1) = 1/4$, $p(1, 2) = 1/8$, $p(2, 2) = 1/2$.



      Find the distribution of $xi$, if $eta = i$, $i = 1, 2$.




      What does it mean by the distribution of $xi$? Does this mean that I have to say that




      $p(xi, 1) = 1/8 + 1/8 = 1/4$ and $p(xi, 2) = 1/8 + 1/2 = 3/4$




      I suspect that it has to do something with joint CDF, but I have no idea how to derive it from the data that I was given.

      Any kind of help would be appreciated.




      probability probability-distributions




      share|cite|improve this question













      I'm having trouble with this particular problem.




      Let the random vector $(xi, eta)$ has the following joint distribution law
      $p(1, 1) = 1/8$, $p(2, 1) = 1/4$, $p(1, 2) = 1/8$, $p(2, 2) = 1/2$.



      Find the distribution of $xi$, if $eta = i$, $i = 1, 2$.




      What does it mean by the distribution of $xi$? Does this mean that I have to say that




      $p(xi, 1) = 1/8 + 1/8 = 1/4$ and $p(xi, 2) = 1/8 + 1/2 = 3/4$




      I suspect that it has to do something with joint CDF, but I have no idea how to derive it from the data that I was given.

      Any kind of help would be appreciated.





      probability probability-distributions





      share|cite|improve this question












      share|cite|improve this question




      share|cite|improve this question








      edited Jul 29 at 11:47









      Cornman

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      2,30021027









      asked Jul 29 at 11:35









      Linuxpepe69

      82




      82




















          1 Answer
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          I think you are being asked to find conditional probability.



          For example,



          $$P(xi=1|eta=1)=fracP(xi=1,eta=1)P(eta=1)$$ and $$P(xi=2|eta=1)=fracP(xi=2,eta=1)P(eta=1)$$






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            1 Answer
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            1 Answer
            1






            active

            oldest

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            active

            oldest

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            active

            oldest

            votes








            up vote
            0
            down vote



            accepted










            I think you are being asked to find conditional probability.



            For example,



            $$P(xi=1|eta=1)=fracP(xi=1,eta=1)P(eta=1)$$ and $$P(xi=2|eta=1)=fracP(xi=2,eta=1)P(eta=1)$$






            share|cite|improve this answer

























              up vote
              0
              down vote



              accepted










              I think you are being asked to find conditional probability.



              For example,



              $$P(xi=1|eta=1)=fracP(xi=1,eta=1)P(eta=1)$$ and $$P(xi=2|eta=1)=fracP(xi=2,eta=1)P(eta=1)$$






              share|cite|improve this answer























                up vote
                0
                down vote



                accepted







                up vote
                0
                down vote



                accepted






                I think you are being asked to find conditional probability.



                For example,



                $$P(xi=1|eta=1)=fracP(xi=1,eta=1)P(eta=1)$$ and $$P(xi=2|eta=1)=fracP(xi=2,eta=1)P(eta=1)$$






                share|cite|improve this answer













                I think you are being asked to find conditional probability.



                For example,



                $$P(xi=1|eta=1)=fracP(xi=1,eta=1)P(eta=1)$$ and $$P(xi=2|eta=1)=fracP(xi=2,eta=1)P(eta=1)$$







                share|cite|improve this answer













                share|cite|improve this answer



                share|cite|improve this answer











                answered Jul 29 at 11:39









                Siong Thye Goh

                76.9k134794




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