Hi all Just a few queries on chapter 6 (CT3-06): 1) Is convolution only for independent variables? (CT3-06 Section 3) 2) On pages 30-31, the notes say "This method can also be used to obtain the MGF of a binomial / negative binomial distribution." How is this done? 3) On pages 31 and 34, how does one find the mean and variance of a sum of variables? Thank you
Yes. Otherwise we could split the probabilities (or PDFs) up. I think you mean PGFs. For the binomial derive the PGF of a bernoulli. Use the fact that Bin(n,p) is the sum of n Bernoullis. So all this into the formula at the bottom of page 29. They're using the formulae from page 27 (ie for independent RV's just sum them).
