15.3 Exercise 35

The number N of noise bursts on a data transmission line in a period $\left(0 , t\right]$ is Poisson $\left(\mu t\right)$. The number of digit errors caused by the ith burst is Y_i, with the class $\left\{Y_{i} : 1 \leq i\right\}$ iid, $Y_{i} - 1 \sim$ geometric $\left(p\right)$. An error correcting system is capable or correcting five or fewer errors in any burst. Suppose $\mu = 12$ and $p = 0 . 35$. What is the probability of no uncorrected error in two hours of operation?