# Thread: Doubt: Expected Values of Bivariate Random Variables

1. ## Doubt: Expected Values of Bivariate Random Variables

E[X|Y, Z] = E[X|Y]

I am given a problem with this condition. Please tell me what the left hand side term mean?? and what can we write for it??
E[X|Y, Z] = ??
(I expect something in terms of Joint PDF or Conditional PDF.If that cannot be done, please tell me any other way)
I know what to write for E[X|Y]. But what should we write for E[X|Y, Z]?? URGENT!! (Tell me if my question is not clear!!)

2. Originally Posted by devd
E[X|Y, Z] = E[X|Y]

I am given a problem with this condition. Please tell me what the left hand side term mean?? and what can we write for it??
E[X|Y, Z] = ??
(I expect something in terms of Joint PDF or Conditional PDF.If that cannot be done, please tell me any other way)
I know what to write for E[X|Y]. But what should we write for E[X|Y, Z]?? URGENT!! (Tell me if my question is not clear!!)
Hi there. I think (could be wrong after all) that it's something like:

$\mathbb{E}(X|(Y,Z))$,

that is, you treat Y,Z as a random vector. I don't know if this helps but you can condition a variable with respect to any random variable, also vectors.

3. Originally Posted by devd
E[X|Y, Z] = E[X|Y]

I am given a problem with this condition. Please tell me what the left hand side term mean?? and what can we write for it??
E[X|Y, Z] = ??
(I expect something in terms of Joint PDF or Conditional PDF.If that cannot be done, please tell me any other way)
I know what to write for E[X|Y]. But what should we write for E[X|Y, Z]?? URGENT!! (Tell me if my question is not clear!!)[/QUOTE]
E[X|Y,Z] means the expected value of X, given specific values of Y and Z. Saying that is equal to E[X|Y], the expected value of x given a specific value of Z, tells you that X is independent of Z.