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So we were talking about the beta distribution and the gamma distribution separately. And I mentioned that they're connected but we haven't seen, how is beta connected to gamma other than being consecutive letters of the Greek alphabet? So there's one very, very famous example that connects the beta and the gamma in a very neat way. So that seemed like a natural starting point to bring the beta and the gamma together. Another thing we haven't done yet is figure out the normalizing constant for the beta distribution, except in the special cases where we could use Bayes Billiards arguments. So we want to have the normalizing constant in general for beta and gamma. So, here's an example, it's a story that connects the beta and gamma. I call it a bank and post office. You can call it whatever you want. I just like having a concrete example in mind and for some reason I call this the bank post office example. So the idea is you have to go to the bank and do something. You have to go to the post office and do something. Both of them you have to wait in line for some amount of time. And let's define some notation. So let's say first you go to the bank and you wait for a total of X minutes to be served and suppose that X is gamma of a lambda. If a is an integer, I didn't just like randomly write down gamma, there would be a natural interpretation here. If a is an integer, let's gamma five lambda. Remember we saw that the gamma five lambda, you can think of it as the sum of five i.i.d exponential lambda. So that would be like the assumption that everyone, there's five people in line before you and each of them takes an exponential lambda amount of time to be served. And there's only one line and we could wait in line and then eventually your turn. Okay, and then let y be gamma of b lambda same thing. X is how long you wait, that's your waiting time to be served at the bank. And Y is your waiting time at the post office. And we'll assume they're independent. X is independent of Y, that's the assumption. So that's a statement of the set up. Now the question is, first of all, what's the distribution, Of your total waiting time? And let's call that T, T for total. That we already actually know. At least for the integer case. If a and b are integers, this is the sum of a i.i.d exponentials. This is the sum of b i.i.d exponentials. So together they must be a plus b i.i.d exponentials. So just from that story you immediately say that it's gamma a plus b, lambda and we don't have to do anything else. If it's not an integer, you could just to the MGF, that we also did, and just multiply...