Analyzing the Sum of Two Binomial Random Variables
Consider two independent Binomial random variables, X and Y, where X ~ Bin(\(n_1, p\)) and Y ~ Bin(\(n_2, p\)). (a) Show that the sum \(X+Y\) is binomially distributed and write its probability mass function (pmf) in terms of \(n_1, n_2\) and \(p\). (b) In a quality control process, the number of defective items from two […]