Let's say we have $\displaystyle n $ exponential random variables $\displaystyle X_1,X_2, \ldots, X_n $. Now consider the following: $\displaystyle X_1 + X_2 + \ldots + X_n $.

What type of distribution would the sum of $\displaystyle n $ exponential random variables, each with mean $\displaystyle \lambda_i $ have?