Hello,

I have a few questions about a couple of problems that I received in my math class. most of them are probability related

1) "Suppose that you arrive at a train station with one receptionist to find fiver other customers in the station, one being served and the other four waiting in line. You join the end of the line. If the service times are all exponentially distributed with rate whether it is for purchase, refund or exchange, what is the expected amount of time you will spend in the station?" - for this problem, my friend and I thought the answer was 6 because, since the expected value of our random variable X, E(X)= , and since X is exponentially distributed and therefore memoryless, the amount of time it would take for 5 people to be served + the amount of time it would take for you to be served would be 6 times the expected value, i.e. 6.

2) "In an example concerning Cantor-Junkes model of DNA, we showed that pi,i(n)=41+43(14a)n and pj,i(n)=4141(14a)n, where pi,i(n) and pj,i(n) denote the transition probability from i to i and i to j for i not equal to j respectively, hold for case n = 1, and if they hold for the case n, then the first equation holds for the case n+ 1. Show that the second equation also holds for the case n + 1." - apparently this can be done with some careful observations; however, while trying this problem, the only thing we thought we could do was just take the sum of all of the different products of transition probabilities that will successfully arrive at pj,in+1, but, even doing this, we couldn't get to the answer as our sum did not simplify. please help!!

Thank you for your consideration and help.

All the best