A link with transmission rate $R_b[bit/sec]$ is used to forward packets having random size $l[bit]$ which has a geometric PMD:
$p_l(k) = p(1-p)^{k-1}$
Prove that, if $E[l] = \frac{1}{p}$ is large enough the distribution of the packet transmission times can be approximated to an exponential distribution with parameter $\mu = \frac{R_b}{E[l]}$
The transmission time is:
$t_T = \frac{l}{R_b}$
The distribution of $t_T$ should be:
$P[t_T \le a] = P[\frac{l}{R_b} \le a]=P[l\le aR_b ] = 1-(1-p)^{a R_b}$
I would like to know if what I wrote is right and some hints on how to proceed from here...