Examples of pairewise independent but not independent continuous random variables By considering the set $\{1,2,3,4\}$, one can easily come up with an example (attributed to S. Bernstein) of pairwise independent but not independent random variables. 
Counld anybody give an example with continuous random variables? 

The continuous analog of the Bernstein example: Divide up the unit cube into eight congruent subcubes of side length $1/2$. Select four of these cubes: Subcube #1 has one vertex at $(x,y,z)=(1,0,0)$, subcube #2 has one vertex at $(0,1,0)$, subcube #3 has one vertex at $(0,0,1)$, and subcube #4 has one vertex at $(1,1,1)$. (To visualize this, you have two layers of cubes: the bottom layer has two cubes in a diagonal formation, and the top layer has two cubes in the opposite diagonal formation.)
Now let $(X,Y,Z)$ be uniform over these four cubes. Clearly $X, Y, Z$ are not mutually independent, but every pair of variables $(X,Y)$, $(X,Z)$, $(Y,Z)$ is uniform over the unit square (and hence independent).
