Assume $X_i$ probability density function is : $$f(x,\lambda)=\Bbb{I}_{(0,\infty)}(x)\lambda \exp(-\lambda x)$$
how to find the probability density function of $\sum X_i$ ? The result is $$\Bbb{I}_{(0,\infty)}(x)\frac{1}{(n-1)!}\lambda^nx^{n-1} \exp(-\lambda x)$$
But I don't know how to find it.
where $\Bbb{I}_{A}(x)=\begin{cases} 1, & x \in A \\ 0, & x\not\in A \end{cases}$
