CT3 Sept 2013 Q4a

Hi all,

With this question, the solutions pull out the term when x=0, so that the summation changes from (x=1, inf) to (x=0, inf)

Is there a requirement for expectations to always be defined over (x=0, inf), or has this just been done to match the format required in the question? ie if i was simply asked for the expectation could i have kept it as
sum(x=1,inf((-\theta^x/(log(1-\theta))

Thanks

 

also sorry to add to this, but how does this turn into \theta/(1-\theta)ln(1-\theta)?

 

managed to figure this part out, so just need help with why we would change the sum limits to (0,inf) please

 

Thank you so much!!