The cumulative distribution of the random variable X X is given by F ( x ) =

The cumulative distribution of the random variable $X$ is given by

$F\left(x\right)=(1-p^{x+1})I_{\{0,1,2,\dots \}}\left(x\right)$, for some choice of $p\in (0,1)$.

a. Find the density function of the random variable $X$.

b. What is the probability that $x\le 8$ if $p=.75$ ?

c. What is the probability that $x\le 1$ given that $x\le 8$ ?