Hi all, Am just trying to read between the lines of the MGF proofs. I seem to be ok with all the discrete ones except negative binomial. Its just the step between pe^t*Σ(x-1)C(k-1)*(qe^t)^x-k to becoming =(pe^t)^k*(1-qe^t)^-k appreciate this must be an application of the binomial series, but i cant understand how! Please could someone explain? Thanks, Molly
Hi Molly It is from the binomial expansion, p2 of the Orange Tables, (1+x)^p, here x=-qe^t and p=-k, it's where its name is from the negative binomial! Hope this helps
Ah great thank you, in the exam are we expected to be able to recognize binomial series and apply them in this way or is knowing this proof sufficient?
Given that the exams are now online - it's unlikely that you'd be asked to prove a result that is given in the notes. As you'd then just be copying it. However, applying a binomial series to sum another MGF could be asked.
