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? 

Here's a potentially very simple construction for $k$-wise independent random variables, uniformly distributed on $[0, 1]$ (though admittedly I didn't work it out very carefully so hopefully the condition checks out)? There is a standard way of constructing discrete $k$-wise independent random variables: let $X_1,\ldots, X_{k}$ be uniform independent rvs drawn from $F$, $F$ a finite field of order $q$ ($q$ sufficiently larger than $k$, of course). Then, for $u\in F$, let $Y_u = X_1 + uX_2+\cdots + u^{k-1}X_k$. Then, the random variables $\{Y_u : u\in F\}$ are $k$-wise independent.
Now, just divide $[0, 1]$ into $q$ evenly spaced subintervals. Let $Z_u$ be uniform from the $Y_u$th subinterval. The rvs $\{Z_u : u\in F\}$ are $k$-wise independent (their joint CDF would decompose as the product of the individual CDFs, since the $\{Y_u\}$ are $k$-wise independent), and are uniform over $[0, 1]$ since each $Y_u$ is uniform over $F$.
