Can you include as much detail in your explanation as possible? Thank you so much!

Let X1, ... , Xn be independent and exponentially distributed random variables with parameter lambda. Consider the sum Yn = ni=1 Xi. Show that Yn has a gamma distribution with parameters (n, lambda). Let X1, ... , Xn be independent and exponentially distributed random variables with parameter lambda. Consider the sum Yn = ni=1 Xi. Show that Yn has a gamma distribution with parameters (n, lambda)