In Ch3 , I can't understand some stage of proof of mgt of some distribution. My CMP is 2022 version. If possible,please tell me which theorems or how to replace the derivations to reach these conclusions. 1.In page 9 of CH3, I don't understand why the second row becomes the third row of M_x(t) of proof of Negative binomial(k,p). It seems like binomial series, but I can't understand but I don't understand what's going on between the lines. 2.In page 9 of CH3, I can't understand what happened between the first equal sign and the second equal sign in Possion. I can't understand how it change from sum(inf,0)lamda*exp(t))^x/x! to exp(-lamda)*exp(-lamda*exp(t)).
Hi Ykai 1. The summation is replaced by the binomial expansion of (1+x)^p, with x=-qe^t and p=-k, from p2 of the Tables 2. The summation is replaced by the exponential expansion of e^x, with x=lambda*e^t , from p2 of the Tables Hope this helps Andrea
