When a two-way paging system transmits a message, the probability that the messa

Question

When a two-way paging system transmits a message, the probability that the message will be received by the pager it is sent to is p. When the pager receives the message, it transmits an acknowledgment signal (ACK) to the paging system. If the paging system does not receive the ACK, it sends the message again. (a) Now assume that p = 0.75, and define N to be the number of times that the message was sent by the pager. Then N is a geometric its parameter(s). (0.75 ) random variable. That is, identify the type of random variable and (b) Find the PMF of N usiasmon 0 n = 1,2,3, Py(n) = otherwise (c) The paging company wants to limit the number of times it has to send the same message. It has a goal of PIN S 6]2 0.98. What is the minimum value of p necessary to achieve this goal?

Explanation / Answer

c)P(N<=6)>=0.98

therefore P(N>6) <=1-0.98

P(N>6) <=0.02

(1-p)6 <0.02

(1-p)<0.021/6

p>1-.521

p>=0.479

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