For many problems in mathematics and theoretical computer science, it is of interest to estimate concentration of sums of heterogenous boolean random variables. This note shows some new results obtained through majorization theory with computer-aided proof in SymPy. Results The Poisson Binomial distribution is defined for as$$Y = \sum_{i=1}^n X_i,\quad X_i \sim \mathrm{Bern}(p_i).$$ We are …