1. ## Exponential Random Variables

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?

2. Originally Posted by shilz222
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?
Are the random variables continuous or discrete?

For starters, you might want to read through this. The continuous stuff is in 7.2. This might also shed light on my reply to your hyperexponential question (if more light is needed .....)

So work it for $\displaystyle Z_1 = X_1 + X_2$. Then use that result to get $\displaystyle Z_2 = Z_1 + X_3$. Then use that result to get $\displaystyle Z_3 = Z_2 + X_4$. etc. For a result when the random variables are discrete, read through this.