Problem Sheet 9 exercise 4

Problem Sheet 9 exercise 4

par Giorgio Facelli,
Nombre de réponses : 2

Hello,

I was looking over the solution of exercise 4 in problem sheet 9 and I don't seem to understand a part of it. In particular, when the second approach to finding the solution is explained, there is this calculation in the image. I don't really understand the last equality. How are we allowed to change the second summation and product bounds from T to (t-1)? I can't really get my head around. Thanks in advance for the help.


Best regards,

Giorgio Facelli


Annexe Screenshot from 2023-05-04 18-53-01.png
En réponse à Giorgio Facelli

Re: Problem Sheet 9 exercise 4

par Alireza Modirshanechi,
Hi Giorgio,
This is a very good question. The trick is to realize one can break the sum into multiple smaller ones and used the fact that probability distributions are normalized.
We updated the solution with an extra explanation; here is a screenshot of that part:
Week 9 Exc 4