Hi, Could someone please explain how to use the iterative formula? For example, in both part 2 and 3 of Q1.6, the iterative formula is used to make calculating the answer faster. Basically I can't see how its used and it doesn't seem to be in the core reading. I'm sorry if this has been asked already. A rough overview would be really helpful. Thanks, Tom
The recursive formula is given for the NBin on page 8 of Chapter 4 but (surprisingly) not for the binomial. Essentially the formula on p8 says: \(P(X=x) = \frac{x-1}{x-k} (1-\theta) P(X=x-1)\) So if you know the answer for P(X=x-1) then you can calculate P(X=x). So we calculated P(X=4) in Q1.6(ii) as 0.0081. Hence using the formula with x=5 (and k=4 and \(\theta = 0.3\)) we get: \(P(X=5) = \frac{5-1}{5-4} (1-0.3) P(X=4)\)
