Wat is Exchangeability, permutation test?

Random variables $Y_1, \dots, Y_n$ are exchangeable (exchangeability) if the law of $(Y_{\pi(1)}, \dots, Y_{\pi(n)})$ is the same for every permutation $\pi$. A permutation test of the null that $Y$ is independent of $X$ compares a statistic $T(X, Y)$ with its values over random permutations of $Y$; the $p$-value is $(1 + \#\{T(X, Y_\pi) \ge T(X, Y)\})/(1 + P)$ for $P$ permutations.