Suppose there are n stations in a slotted LAN. Each station attempts to…
2017
Suppose there are n stations in a slotted LAN. Each station attempts to transmit with a probability P in each time slot. The probability that only one station transmits in a given slot is _______.
- A.
nP(1 – P)n – 1
- B.
nP
- C.
P(1 – P)n – 1
- D.
nP(1 – P)n – 1
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Show answer & explanation
Correct answer: A
Answer: n × P × (1 − P)^(n − 1)
Derivation:
There are n choices for which station is the sole transmitter.
The chosen station transmits with probability P.
Each of the other n − 1 stations does not transmit with probability (1 − P), so together that is (1 − P)^(n − 1).
Multiply these factors: n × P × (1 − P)^(n − 1).
Note: P × (1 − P)^(n − 1) is the probability for a specific station to be the sole transmitter; multiplying by n accounts for any one of the n stations.
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