e both <span class="math inline">\(\text{Bin}(N,0.5^P)\)</span> distributed.<br> Bernoulli distributions are subGaussian with subGaussian parameter <span class="math inline">\(\sigma^2=0.25\)</span>, regardless of the success probability <span class="math inline">\(p\)</span>. Thus <span class="math inline">\(\text{Bin}(N,p)\)</span> distributions are subGaussian with subGaussian parameter <span class="math inline">\(\sigma^2=0.25N\)</span>. Being subGaussian implies that a distribution has nice tail bounds