1. A coin is randomly selected from a group of ten coins, the nth coin having a probability n/10 of coming up heads. The coin is then repeatedly ?ipped until a head appears. Let N denote the number of ?ips necessary. What is the probability dis- tribution of N? Is N a geometric random variable? When would N be a geometric random variable; that is, what would have to be done differently?
2. You are invited to a party. Suppose the times at which invitees are independent uniform (0,1) random variables. Suppose that, aside from yourself, the number of other people who are invited is a Poisson random variable with mean 10.
(a) Find the expected number of people who arrive before you.
(b) Find the probability that you are the nth person to arrive.