Question: 10. [15 marks] In a wireless automatic meter reading system, a base station sends out a wakeup signal to nearby electric meters. On hearing the

10. [15 marks] In a wireless automatic meter reading system, a base station sends out a wakeup signal to nearby electric meters. On hearing the wakeup signal, a meter transmits a message indicating the electric usage. Each message is repeated 8 times. (a) If a single transmission of a message is successful with probability p, what is the PMF of N , the number of successful message transmissions? (b) I is an indicator random variable such that I = 1 if at least one message is transmitted success- fully; otherwise I = 0. Find the PMF of I. (c) What is the minimum value of p such that the probability that I = 1 is greater than 95% 7

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