1. ## What to study?

My probability skills are rusty and I simply wish to enquire the precise set of areas I need to brush up in order to solve the following problem:

Suppose users share a l Mbps link for packet transmission. Each user requires 100 Kbps when transmitting, but each user only has packets to transmit 10 percent of the time.
(a) What is the probability that at any given time, a particular user has something to transmit?
(b) Suppose there are 50 users. What is the probability that at any given time, n out of the 50 users have something to transmit?
(c) For 50 users, find the probability that there are 11 or more users transmitting simultaneously. [You can use an approximation such as the Normal approximation to the binomial; you can also do a more exact computation by using a recursive evaluation of binomial probabilities, starting from evaluation of P(0 of 50 users active)].

You can assume I fathom the communication technology aspect of the question but am extremely clueless on the probabity side.

Best,
wirefree

2. Originally Posted by wirefree

My probability skills are rusty and I simply wish to enquire the precise set of areas I need to brush up in order to solve the following problem:

Suppose users share a l Mbps link for packet transmission. Each user requires 100 Kbps when transmitting, but each user only has packets to transmit 10 percent of the time.
(a) What is the probability that at any given time, a particular user has something to transmit?
(b) Suppose there are 50 users. What is the probability that at any given time, n out of the 50 users have something to transmit?
(c) For 50 users, find the probability that there are 11 or more users transmitting simultaneously. [You can use an approximation such as the Normal approximation to the binomial; you can also do a more exact computation by using a recursive evaluation of binomial probabilities, starting from evaluation of P(0 of 50 users active)].

You can assume I fathom the communication technology aspect of the question but am extremely clueless on the probabity side.

Best,
wirefree
a) I am unsure, but I would say it's simply 10 percent.

b) $\displaystyle {50 \choose n} \left( 0,1 \right) ^{n} \left( 0,9 \right) ^{50 - n}$

c) $\displaystyle 1 - \sum_{n = 0} ^{10} {50 \choose n} \left( 0,1 \right) ^{n} \left( 0,9 \right) ^{50 - n}$ (We are calculating the complement of LESS than 11 here.)

3. Originally Posted by janvdl
a) I am unsure, but I would say it's simply 10 percent.

b) $\displaystyle {50 \choose n} \left( 0,1 \right) ^{n} \left( 0,9 \right) ^{50 - n}$

c) $\displaystyle 1 - \sum_{n = 0} ^{10} {50 \choose n} \left( 0,1 \right) ^{n} \left( 0,9 \right) ^{50 - n}$ (We are calculating the complement of LESS than 11 here.)
Appreciate the response.

However, solutions were not requested for in my initial post.

Please list the precise set of topics that I need to study in order to be able to address such questions.

Best,
wirefree

4. ## I don't know.

If you are interested in probability, you can find numerous sources easily. If you are not familiar with probability at all, start with some discrete math texts, are even a dedicated text (probability only), or go all the way and get an introductory text for statistics.

Take your choice: with or without calculus.

If you want to apply probability theory to communications theory, you can peruse 40 years of articles, but that probably is a complete waste of time.

------------------------------------------------

What I don't understand is how one is supposed to know the probability that any user is going to transmit without knowing the typical traffic or user-needs constraints.

Maybe I just don't understand the technology.

What is the probabiltiy of winning the lottery?

That can be easily solved numerically.

What is the probability that some person out of a set of persons is going to play the lottery anyway at some particular time?

Beats me, unless I know the person's habits.

I see someone gave you an answer but not to your question.

I don't understand their answer myself.

5. Originally Posted by wirefree
Appreciate the response.

However, solutions were not requested for in my initial post.

Please list the precise set of topics that I need to study in order to be able to address such questions.

Best,
wirefree
Well this question was based on the Binomial Distribution

Other topics you might want to read up on:
Negative Binomial Distribution
Geometric Distribution
Hypergeometric Distribution
Poisson Distribution
Exponential Distribution

EDIT: I must add that you can search wikipedia for all these. Just post things you don't understand here, and we'll do our best to help you with it

I see someone gave you an answer but not to your question.

I don't understand their answer myself.
You sir have replied with an utterly useless message. Besides the fact that you only said he could easily find numerous sources, the rest of your reply consists of utter jargon about how you don't understand the concept. Your reply is presented in a messy fashion, with each single sentence in a line of its own. For what reason, if i may ask??

7. Hello,

If you are interested in probability, you can find numerous sources easily. If you are not familiar with probability at all, start with some discrete math texts, are even a dedicated text (probability only), or go all the way and get an introductory text for statistics.

Take your choice: with or without calculus.

If you want to apply probability theory to communications theory, you can peruse 40 years of articles, but that probably is a complete waste of time.

------------------------------------------------

What I don't understand is how one is supposed to know the probability that any user is going to transmit without knowing the typical traffic or user-needs constraints.

Maybe I just don't understand the technology.

What is the probabiltiy of winning the lottery?

That can be easily solved numerically.

What is the probability that some person out of a set of persons is going to play the lottery anyway at some particular time?

Beats me, unless I know the person's habits.

I see someone gave you an answer but not to your question.

I don't understand their answer myself.
Stop taking what you think for a general matter. Don't you think that the OP would know better than you do ?

Besides that,
does not mean "Please enter the beginning of what you're saying"...

And use the [QUOTE][/QUOTE] tags when you want to quote something... (I'm refering to previous threads ^^)

If you are interested in probability, you can find numerous sources easily.
If they knew how then they would not be asking here. As it is this part of you post is a waste of bandwidth as you do not tell him how to find such sources.

Next time give some links, other references or explain the use of Google.

RonL

9. ## Bandwidth, Solutions, Where To Look

Ok.

If I asked you what is the meaning of the math answer, how much would you go out of your way to teach me these things over the Internet, on my demand? Could you arrange to send compact lessons with feedback to make sure I was getting it?

Your reward could be messages such as "I like you better than I like that useless responder who did not follow up my demands to my complete satisfaction." That's what is coming through from the originator, which I shall ignore in the future.

The orignator is demanding and judgemental without adding anything. That's how it goes. The originator may be brilliant and a credit to the human race, like Isaac Newton, but unfortunately lacks social graces that make life more meaningful and enjoyable, also like Isaac Newton.

I see a reply not unlike, "I don't like what you have offered and you can keep your opinion to yourself, you useless low-order being."

The originator could have just ignored it or have tried being honest with, "I have only meager skills to solve this applied math problem, and I want someone to make me smarter for this particular problem and no other as I have no interest in educating myself in probability theory and statistics."

I am not applying for a job here, so take it or leave it.

There are six billion people on this planet. It does not pay to empower the antisocial manipulating variety. Plug that into game theory and see what you get.

Ok.

If I asked you what is the meaning of the math answer, how much would you go out of your way to teach me these things over the Internet, on my demand? Could you arrange to send compact lessons with feedback to make sure I was getting it?
Have you noticed the name? "Math Help Forum"

The name of the forum is not: "Reply-with-useless-information forum".

For your information the majority of the people here love math, and also like teaching it to others. I can name a few members who really go out of their way to help others understand, with clear explanations and a friendly personality.

Your reward could be messages such as "I like you better than I like that useless responder who did not follow up my demands to my complete satisfaction." That's what is coming through from the originator, which I shall ignore in the future.
I have absolutely no idea what you are jabbering on about.

The orignator is demanding and judgemental without adding anything. That's how it goes. The originator may be brilliant and a credit to the human race, like Isaac Newton, but unfortunately lacks social graces that make life more meaningful and enjoyable, also like Isaac Newton.
If you are saying I lack social skill, well i think you are full of it. In fact I think you lack the mathematical side. Why not join a general discussion forum rather? One where you can be as social as you like, and type all kinds of non-sensible sentences.

I see a reply not unlike, "I don't like what you have offered and you can keep your opinion to yourself, you useless low-order being."
I do not regard you as a low-order being, but your posts go off topic, and you help out very very little when you reply.

The originator could have just ignored it or have tried being honest with, "I have only meager skills to solve this applied math problem, and I want someone to make me smarter for this particular problem and no other as I have no interest in educating myself in probability theory and statistics."
If by the originator you mean the original poster, i think he understands the concept of the thing. Unlike you who does not understand even the most basic computer terms. And then you blabber on about it in a post.

I am not applying for a job here, so take it or leave it.
I wanted to post something here but I think I'll keep it to myself.

There are six billion people on this planet. It does not pay to empower the antisocial manipulating variety. Plug that into game theory and see what you get.
I am not manipulating anyone in any way. I do not see myself as important, or better than others. What I see is someone who has an arrogant personality and is determined to make useless posts.

11. Banned

Though I disagree with you janvdl, Bradley has been helpful some times
But when we suggested to him to learn bits of latex language, ... he said he had other matters than spending time to it (if I've understood well ~)

12. Originally Posted by Moo
Banned

Though I disagree with you janvdl, Bradley has been helpful some times
But when we suggested to him to learn bits of latex language, ... he said he had other matters than spending time to it (if I've understood well ~)
While I do not want to argue with you, the majority of his posts were not.

13. Originally Posted by janvdl
While I do not want to argue with you, the majority of his posts were not.
Hey, I said "some times"

14. Originally Posted by Moo
Hey, I said "some times"
I have just reviewed his postings and there is something odd about the majority of them.

RonL

15. Originally Posted by CaptainBlack
I have just reviewed his postings and there is something odd about the vast majority of them.

RonL
In a few of them he ended up with religion, by going way off topic... Or are you thinking of something else?

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