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 P: 21 Hi, Can anyone derive the sum of exponentially distributed random variables? I have the derivation, but I'm confused about a number of steps in the derivation. Here they are: Random variable x has the PDF, $$f(s) = \left\{ \begin{array}{c l} e^{-s} & if s \ge 0 \\ 0 & otherwise \end{array} \right.$$ Let $$X_1, X_2, .... , X_n$$ be independently exponentially distributed random variables. The PDF of the sum, $$X_1 + X_2 + ..... +X_n$$ is $$q(s) = e^{-(s_1+s_2+....+s_n)}$$ where s $$s \ge 0$$ => $$\int_{a \le s_1+s_2+....+s_n \le b} q(s) ds$$ = $$\int_{a \le s_1+s_2+....+s_n \le b} e^{-(s_1 + .... + s_n)} ds$$ Can anyone explain this stage? Going from the above integral to the following integral? = $$\int^b_a e^{-u} vol_{n-1} T_u du$$ where $$T_u = [s_1+ .... + s_n = u]$$ What would $$vol_{n-1}$$ be here?