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,

Thanh