Find the expected number of people

Reference no: EM131005838

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.

Reference no: EM131005838

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