- 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. > X is a 2N*1 dim complex vector and is related to a N*1 dim vector Y

Murat,

> 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.

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 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 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 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]