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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
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.
• ... 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.
• 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]
• 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]
• 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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