1. ## discrete probability problems

hello,
can anyone in the forum help me with these 3 discrete probability problems?
(attached in a pdf document)
cheers

2. For part a of the first question you need to find $\displaystyle C$ such that

$\displaystyle \sum_{r=1}^{\infty} p_k(r)=\sum_{r=1}^{\infty} C(1-P)^{r-1} =1$

as the sum of the pmf should be $\displaystyle 1$. For $\displaystyle 0<P<1$ this is a convergent geometric series, and you should be able to write down
Note $\displaystyle \sum_{r=0}^{\infty} q^r = \frac{1}{1-q}, \ \ \mbox{for all }0<q<1$