Suppose I have two statements:
Statement 1: Random variable Z is the common cause for random variable X and Y (Z causes both X and Y)
Statement 2: Random variable X and Y are (conditionally) independent given Z.
What's the relationship between Statement 1 and Statement 2? Does Statement 1 imply statement 2, or does statement 2 imply statement 1, or they have other relationships?
Example: Z could be the grade level(or age) for a primary school student, X could be his height, Y could be his math ability. Thanks!