in Computer Networks recategorized by
1,415 views
1 vote
1 vote

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____

  1. $nP(1-P)^{n-1}$
  2. $nP$
  3. $P(1-P)^{n-1}$
  4. $n^P (1-P)^{n-1}$
in Computer Networks recategorized by
1.4k views

5 Answers

3 votes
3 votes
Best answer

It can be derived using Binomial theorem  of probability 

NCi((p)i(1-p)n-i 

Now 1 stations is sending with probability P ,and n-1 stations are not sending with probability 1-p

Now the probaility is= nC1 (p)1(1-p)n-1

=np(1-p)n-1

so a is correct answer here

selected by
4 votes
4 votes

A) Np(1 – p)N-1.

 the probability a  node has a success is p(1 – p)N-1. Because there are N nodes, the probability that any one of the N nodes has a success is Np(1 – p)N-1.

0 votes
0 votes

It can be derived using Binomial theorem  of probability 

NCi((p)i(1-p)n-i 

Now 1 stations is sending with probability P ,and n-1 stations are not sending with probability 1-p

Now the probaility is= nC1 (p)1(1-p)n-1

=np(1-p)n-1

so a is correct answer here

0 votes
0 votes

The probability that a particular station transmits and no body else transmits = $p*(1-p)^{(n-1)}$
The probability that any station can transmit = n*(probability that a particular station transmits)

= $\binom{n}{1}*p*(1-p)^{(n-1)}$

Answer:

Related questions