A transmitter is trying to send a packet to a receiver. With each transmission attempt, the pa received with chance p. If the packet is received, the receiver sends an acknowledgement of the p which the transmitter receives with chance q. If the packet is not received, the receiver sends no If an acknowledgement is received by the transmitter it deems the packet transmission as "don the transmitter fails to successfully receive an acknowledgement by the time it would be due to 1

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.3: Conditional Probability; Independent Events; Bayes' Theorem
Problem 39E: The following problem submitted by Daniel Hahn of Blairstown, Iowa, appeared in the Ask Marilyn...
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. A transmitter is trying to send a packet to a receiver. With each transmission attempt, the packet is
received with chance p. If the packet is received, the receiver sends an acknowledgement of the packet,
which the transmitter receives with chance q. If the packet is not received, the receiver sends nothing.
If an acknowledgement is received by the transmitter it deems the packet transmission as “done." If
the transmitter fails to successfully receive an acknowledgement by the time it would be due to arrive,
it proceeds with a new transmission attempt.
(a) Let X be the number of transmission attempts it takes on the transmitter's part until the trans-
mitter deems the packet transmission as “done." What is the PMF of X?
(b) What is E[X]?
Transcribed Image Text:. A transmitter is trying to send a packet to a receiver. With each transmission attempt, the packet is received with chance p. If the packet is received, the receiver sends an acknowledgement of the packet, which the transmitter receives with chance q. If the packet is not received, the receiver sends nothing. If an acknowledgement is received by the transmitter it deems the packet transmission as “done." If the transmitter fails to successfully receive an acknowledgement by the time it would be due to arrive, it proceeds with a new transmission attempt. (a) Let X be the number of transmission attempts it takes on the transmitter's part until the trans- mitter deems the packet transmission as “done." What is the PMF of X? (b) What is E[X]?
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