An event independently occurs on each day with probability p. Let N(n) denote the total number of events that occur on the first n days, and let Tr denote the day on which the rth event occurs.

(a) What is the distribution of N(n)?

(b) What is the distribution of T1?

(c) What is the distribution of Tr?

(d) Given that N(n) = r, show that the set of r days on which events occurred has the same distribution as a random selection (without replacement)

of r of the values 1, 2, . . . , n.