If [math]X[/math] and [math]Y[/math] are two independent discrete random variables such that [math]X\sim\text{Bin}(n,p)[/math] and [math]Y\sim\text{Bin}(m,p)[/math]. How do I interpret [math]Z=X+Y\sim\text{Bin}(m+n,p)[/math] as the sum of two functions [math]X[/math] and [math]Y[/math] ?
Suppose that [math]X[/math] and [math]Y[/math] are discrete random variables. What is the meaning of [math]Z=Y+X[/math], which is the sum of two random variables?