The problem is from the Intro to Probability 2nd The problem is here
And here is the answer.
E[Time] = (5 + E[stay of 2nd student] ) * P(1st stays no more than 5 minutes) + (E[stay of 1st | stay of 1st 5] + E[stay of 2nd] ) * P(1st stays more than 5 minutes)
using the memorylessness property of the exponential distribution, E[stay of 1st | stay of 1st 5] = 5 + E[stay of 1st] = 35
I don't understand why not just E[stay of 1st] = 30 mins? Why is 5 here? I think that if the first person stays longer than 5 mins then the effect of the being late would not be calculated. Appreciate if you help!