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.