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In data communication, one method for error control makes the receiver send a positive acknowledgment for every message received with no detected error and a negative acknowledgment for all the others. Suppose that (i) acknowledgments are transmitted error free, (ii) a negative acknowledgment makes the sender transmit the same message over, (iii) there is no upper limit on the number of retransmissions of a message, and (iv) errors in messages are detected with probability p, independently of other messages. On average, how many times is a message retransmitted?
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