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#1 2005-09-12 06:52:17


Conditional independence

Dear all,

I'm doing my thesis and I have question that's quite confusing to figure out. I hope you would help me.

Suppose we have following random variables:

Y1 = X + N1;
Y2 = X + N2;
where X, N1, N2 are independent of each other.

Of course, Y1 and Y2 are dependent and, therefore, p(Y1Y2) # p(Y1)*p(Y2).
However, can I say Y1 and Y2 are conditionally independent given X, and write:

p(Y1Y2|X) = p(Y1|X)*p(Y2|X)  ???

Is that correct? could you give me a confirmation?

Thanks for reading and hope to hear your answer.

Best regards,

#2 2005-09-15 10:49:09

John E. Franklin
Star Member


Re: Conditional independence

I'm sorry no one is answering your question.  It's beyond anything I've ever learned.

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