1.1. A random variable $X\textasciitilde{}Geo(0.2)$.

By first writing in the form $1-P(X\leqk)$, calculate:

(i) $P(X>3)$

(ii) $P(X>4)$

1.2. Calculate:

(i) $(0.8{)}^{3}$

(ii) $(0.8{)}^{4}$

1.3. By comparing your answers to part (a) and part (b), write down the values of $a$ and $b$ that make the following equations correct:

(i) $P(X>11)=(0.8{)}^{a}$

(ii) $P(X\geq20)=(0.8{)}^{b}$