## 2.5 Independence

The notion of independence is important.

Definition 1.1 (Independence) Two rvs $$X$$ and $$Z$$ are said to be independent if $$f_{X,Z}(x,z) = f_X(x) \times f_Z(z)$$, where $$f_X(x)$$ and $$f_Z(z)$$ are the marginal distributions.
Example 2.10 (Independence) In Example 2.8, we see that $$f_{XZ}(x, z) \ne f_X(x) \times f_Z(z)$$, so $$X$$ and $$Z$$ are not independent.
Example 2.11 (Independence) In Example 2.9, the permissable values of $$Y$$ depend on the value of $$X$$, so clearly $$X$$ and $$Y$$ are not independent.