  We prove that, for any jointly stable random variables $X_1, \dots, X_k$ with
zero mean, any $m<k,$ and any even continuous positive definite functions $f$
and $g$ on $\Bbb R^m$ and $\Bbb R^{k-m},$ the random variables
$f(X_1,\dots,X_m)$ and $g(X_{m+1}, \dots,X_k)$ are non-negatively correlated.
We also show another result that is related to an old question of whether
$$P(\max_{1\le i\le k} |X_i|<t) \ge P(\max_{1\le i\le m} |X_i|<t) \
P(\max_{m+1\le i\le k} |X_i|<t)$$ where $X_1,\dots,X_k$ are jointly Gaussian
random variables with zero mean, and $m<k.$ We show that the quantity in the
left-hand side has a local minimum at the point where the random variables
$X_i$ and $X_j$ are independent for any choice of $1\le i\le m$ and $m+1\le
j\le k.$
