Part (i)

(a) pmf = \(\displaystyle p(k) = (1-p)^{k-1} \cdot p \)

(b) is a simple proof.

Part (ii)

(a) \(\displaystyle p(X \ge 4) = (1 -\dfrac{1}{3})^{4-1} = (\dfrac{2}{3})^3 = \dfrac {8}{27} \)

(b) & (c) i dont have an idea of how to attempt, any help is greatly appricated.

Thanks guys