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  • Murat Uysal
    Hello! I appreciate if somebody may help me in solving the following problem. Thanking you in advance. Murat Uysal X is a 2N*1 dim complex vector and is
    Message 1 of 5 , Jun 2, 2000
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      Hello!

      I appreciate if somebody may help me in solving the following problem.
      Thanking you in advance.

      Murat Uysal

      X is a 2N*1 dim complex vector and is related to a N*1 dim vector Y
      by a linear transformation. (i.e Y=AX A: a matrix with appropriate
      dimension)
      X is multivariate Gaussian, then find the following conditional
      expectation given Y.
      E[(X^H)BX |Y]=?
      where X^H denotes the conjugate transpose of X and B is a 2N*2N
      matrix.
    • Noel Vaillant
      ... Murat, By linearity, we need to concentrate E[XiXj|Y]. The problem is solved if we can work out the distribution of X, conditionnally on Y. So we need to
      Message 2 of 5 , Jun 2, 2000
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        > X is a 2N*1 dim complex vector and is related to a N*1 dim vector Y
        > by a linear transformation. (i.e Y=AX A: a matrix with appropriate
        > dimension)
        > X is multivariate Gaussian, then find the following conditional
        > expectation given Y.
        > E[(X^H)BX |Y]=?
        > where X^H denotes the conjugate transpose of X and B is a 2N*2N
        > matrix.

        Murat,
        By linearity, we need to concentrate E[XiXj|Y]. The problem is solved
        if we can work out the distribution of X, conditionnally on Y. So we
        need to compute E[exp(i<u,X>)|AX][u in R^N], knowing that X is 2N
        dimensional, and A is Nx2N [and maybe some further assumption on A].

        I shall try to crack this problem over the week-end :-)


        Regards. Noel.
      • sameer singhania
        Q) two persons l and m decide to meet at a ahotel between 4pm and 5pm on a certain day.They also agree that the one who comes first would wait for the other
        Message 3 of 5 , Sep 19, 2005
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          Q) two persons l and m decide to meet at a ahotel between 4pm
          and 5pm on a certain day.They also agree that the one who
          comes first would wait for the other for 15 minutes.If the person
          does not arrive within the waiting period of 15 minutes,they
          would not meet each other.

          ques 1 probability that L and M meet ?
          ques 2 L arrives at 4 15 pm ,what is the prob that L and M meet
          each other ?

          [Non-text portions of this message have been removed]
        • divang_0quen
          Write an email to me, I will send you the solution since I should draw something on a XY plan. I am too lazy to draw it on this text platform Otherwise, you
          Message 4 of 5 , Oct 4, 2005
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            Write an email to me, I will send you the solution since I should draw
            something on a XY plan. I am too lazy to draw it on this text platform
            Otherwise, you can find the way in Papoulis's book where he gives a
            similar example of the possibility of two trains' meeting at a station.





            --- In probability@yahoogroups.com, "sameer singhania" <cateyed10@r...>
            wrote:
            > Q) two persons l and m decide to meet at a ahotel between 4pm
            > and 5pm on a certain day.They also agree that the one who
            > comes first would wait for the other for 15 minutes.If the person
            > does not arrive within the waiting period of 15 minutes,they
            > would not meet each other.
            >
            > ques 1 probability that L and M meet ?
            > ques 2 L arrives at 4 15 pm ,what is the prob that L and M meet
            > each other ?
            >
            > [Non-text portions of this message have been removed]
          • thanhhahuy
            Check out Papoulis: Probability, Random Variables and Stochastic Processes ..., there is a very similar problem as yours. It is a problem of two trains meeting
            Message 5 of 5 , Oct 5, 2005
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              Check out Papoulis: Probability, Random Variables and Stochastic
              Processes ..., there is a very similar problem as yours. It is a
              problem of two trains meeting each other. YOu should draw something on
              a XY plan and then find the ration between a hexagon and a square to
              find the probablity. it is not difficult but I cannot draw them on
              this text platform.


              --- In probability@yahoogroups.com, "sameer singhania"
              <cateyed10@r...> wrote:
              > Q) two persons l and m decide to meet at a ahotel between 4pm
              > and 5pm on a certain day.They also agree that the one who
              > comes first would wait for the other for 15 minutes.If the person
              > does not arrive within the waiting period of 15 minutes,they
              > would not meet each other.
              >
              > ques 1 probability that L and M meet ?
              > ques 2 L arrives at 4 15 pm ,what is the prob that L and M meet
              > each other ?
              >
              > [Non-text portions of this message have been removed]
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