e disjoint subsamples <span class="math inline">\(\mathcal{S}_+\)</span> and <span class="math inline">\(\mathcal{S}_-\)</span> that are far apart. <br> For perspective, set <span class="math inline">\(P=5\)</span> and <span class="math inline">\(M=100\)</span>. We draw <span class="math inline">\(N=M\times 2^P = 3200\)</span> observations at random from the population. The argument above says that with probability at least <span class="math inline">\(1-4 \exp\left(-2 \cdot 2^{0.1P} \cdot M^{0.1}\right) = 0