Equivalently sj l1 l2 lj for j 1 the ls determine

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Unformatted text preview: n 1 + 1 + · · · + n ≈ n ln(n). 1 2 Memoryless property of geometric distribution Suppose L is a random variable with the geometric distribution with parameter p. Then P {L > k } = (1 − p)k , for k ≥ 0. It follows that for n ≥ 0 and k ≥ 0 : P (L > k + n|L > n) = = = P {L > k + n, L > n} P {L > n} P {L > k + n} P {L > n} (1 − p)k+n (1 − p)n = (1 − p)k = P {L > k }. That is, P (L > k + n|L > n) = P {L > k }, which is called the memoryless property in discrete time. Think of this from the perspective of an observer waiting to see something, such that the total waiting time for the observer is L time units, where L has a geometric distribution. The memoryless property means that given the observer has not finished waiting after n time units, the conditional probability that the observer will still be waiting after k additional time units, is equal to the unconditional probability that the observer will still be waiting after k time units from the beginning. 2.6...
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This note was uploaded on 02/09/2014 for the course ISYE 2027 taught by Professor Zahrn during the Spring '08 term at Georgia Tech.

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