Probability Question: Slotted Aloha

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Discussion Overview

The discussion revolves around a probability question related to the Slotted Aloha protocol, focusing on understanding a specific solution and the underlying probability calculations involved. Participants are seeking clarification on the steps and reasoning necessary to solve the problem, which appears to be homework-related.

Discussion Character

  • Homework-related
  • Exploratory
  • Technical explanation

Main Points Raised

  • Zulfi requests help in understanding a solution he found online but does not provide his own work initially.
  • One participant emphasizes the importance of showing one's own work before receiving assistance, suggesting that Zulfi may not be prepared to ask for help without prior effort.
  • Zulfi expresses difficulty with probability concepts, stating that it is his weak point and that he struggles to solve probability questions.
  • A suggestion is made to describe the sequence of events leading to success in slot 5, indicating a need for a structured approach to modeling the problem.
  • Zulfi presents a probability model involving success and failure across multiple slots, detailing the calculations for slots 1 through 5 and seeking corrections to his approach.
  • Zulfi continues to seek feedback on his calculations, indicating a desire for validation or correction of his reasoning.

Areas of Agreement / Disagreement

The discussion reflects a lack of consensus, as Zulfi's approach and understanding of the problem are questioned, and he is encouraged to clarify his reasoning. Participants have differing views on the appropriateness of seeking help without prior effort.

Contextual Notes

Participants have not resolved the mathematical steps involved in Zulfi's probability calculations, and there are indications of missing assumptions regarding the background knowledge required to tackle the problem effectively.

zak100
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Homework Statement
Suppose four active nodes – nodes A, B, C and D – are competing for access to a channel using slotted ALOHA. Assume each node ha an infinite number of packets to send. Each node attempts to transmit in each slot with probability p. The first slot is numbered slot 1, the second slot is numbered slot 2, and so. What is the probability that node A succeeds for the first time in slot 5?
Relevant Equations
I found a solution which does something like that:
(1-p(A))^4 * P(A).
Can some body please explain me this solution?

Zulfi.
 
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zak100 said:
Can some body please explain me this solution?
Not until you show us your work. How did you derive that solution?
 
Hi,
I got it from internet. I can't understand it. Please guide me.

Zulfi.
 
zak100 said:
Hi,
I got it from internet. I can't understand it. Please guide me.

Zulfi.
That violates our rules. We are not here to feed you answers. We help you to do your own work. If you have done no work other than an Internet search, then you're not ready to ask for help.

What course are you taking? What background do you have that should prepare you to be able to do that homework? Why would you use the Internet instead of using that background?
 
Probability is my weak point. I can't solve probability questions. That's why I am asking help
Zulfi.
 
Describe the whole sequence of events "succeeds for the first time in slot 5".

Once you have a description of the events, you can model them.

What happens at slot 1?
What happens at slot 2?
etc
 
Hi,
Success = P(A)
Failure = 1-P(A)
Slot1= no success= 1-P(A)
Slot2 = no success = 1-P(A)
Slot3 = no success = 1-P(A)
Slot4 = no success = 1-P(A)
Probability from 1 to 4 = (1-P(A))^4
Slot 5 = Success of A but failure of other nodes = P(A) * (1-P(B)) * (1-P(C)) * (1-P(D))

Total probability = (1-P(A))^ 4 * P(A) * (1-P(B)) * (1-P(C)) * (1-P(D))

I think I am very close to the answer. Please tell me how to correct the answer?

Zulfi.
 
Hi,
Still waiting for your correction.

Zulfi.
 

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