1.  disjoint

2. random graph models; adjacency matrix

3. Eqns. (2.2), (2.7)

4. 

# P(L_6 = 1 | L_5 = 1) = P(1 person alights and 1 person boards or 0
person alights and 0 person boards at stop 6 | L_5) 

# = P(1 person alights and 1 person boards at stop 6 | L_5) + P( 0
person alights and 0 person boards at stop 6 | L_5) =

0.2*0.4 + 0.8*0.5

5. 

nreps <- 10000; nstops <- 8; count <- 0
for (i in 1:nreps) {
   passengers <- 0
   alight <- 0
   for (j in 1:nstops) {
      if (passengers > 0) 
         for (k in 1:passengers) 
            if (runif(1) < 0.2) {
               passengers <- passengers - 1
               alight <- alight + 1
            }
      newpass <- sample(0:2,1,prob=c(0.5,0.4,0.1))
      passengers <- passengers + newpass
   }
   if (alight == 3) count <- count + 1
}
print(count/nreps)