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An event independently occurs on each day with probability p. Let N(n) denote the total number of events that occur on the ?rst 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?

(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.

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Statistics and Probability, Statistics

Category:- Statistics and Probability
Reference No.:- M91721555

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