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?

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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?
Transcribed Image Text: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?
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