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A variation on a familiar theme: A packet is received correctly by an end user with...

A variation on a familiar theme: A packet is received correctly by an end user with probability p. To increase the likelihood that an important message is received, the packet is sent repeatedly N times. Let random variable X be the number of copies received correctly by the end user.

a) Find the PMF PX(x).

b) If p = 0.9, how large should N be to ensure that with probability 0.99 at least one

copy of the message is received?

Yet another variation: A better packet switched network employs the concept of acknowledgment. When the end user’s device receives a packet correctly it sends an acknowledgment to the sender. Here too, a packet is received correctly with probabilityp, but the sender keeps sending copies of a given packet until a copy is correctly received (signaled by acknowledgment). Let random variable N be the number of times the same message packet is sent.

c) Find the PMF PN (n).

d) To avoid excessive delays (too many repeated transmissions of same packet), it is required that the network maintain P[N < 4] > 0.95. Find the minimum value of pthat will satisfy this requirement

math   Statistics-And-Probability   
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