Math/ Computer Networking problem

urahonky

Hey guys.

Studying for my Computer Networking exam tomorrow like a good boy, and I've run into something. I am checking my answers using Cramster, and everything's checking out except this one problem.

I realize that these problems are all user entered and they could be wrong but I have my doubts.

Basically I am doing Statistical Multiplexing using packet switching.

This: http://mathworld.wolfram.com/BinomialDistribution.html is the site with the information. At the very top there's a formula. I don't want to have to try and type it so if you could look there that would be great.

Okay. So basically these are the numbers I've figured out:

p = 0.1
n = 11
N = 40

So I plug them all in and do the magic dance and I get: 0.0010888882. Sounds good, except I'm looking at the Cramster answer and it says: "Probability of 11 or more hosts transmitting = 0.00146972" which is completely different from mine and I AM DIEING HERE. All I have to do is plug in the numbers right? What the hell am I doing wrong? Why am I getting such a different number?

I used google's calculator then I busted out my TI-84+ and got the same answer. Please, someone help me. How are they getting their number?

This is the Cramster answer (with equation):

Marty81

Without knowing exactly what the problem asks, I'll guess that the problem is here:

urahonky wrote: »

"Probability of 11 or more hosts transmitting =

What you computed is the probability of exactly 11 transmitting.

So you also need to compute the probability of 12 transmitting, and 13 transmitting, and so on, and add them all up.

urahonky

Ahh yes. I see. This is why I hated Calculus because I don't like to actually read the problems fully.

Is there an easy way to get an answer to this without a computer? I realize if I typed that into Mathematica or Matlab I'd get an answer in two seconds, but how would I do that on the calculator? Just type in 11 for n, then 12 for n, and just keep adding those answers together till I get to 40? That will get tedious really fast.

urahonky

Hmm, it looks like when I add up n=11 -> n=15 it gets to the answer given so each addition after that is probably mathematically insignificant.

Marty81

I guess you could write a little calculator program to do that for you, but no, there's really no easier way.

You can estimate the answer using the central limit theorem and the area under the bell curve, but if you want exact answers, there's no other way.

urahonky

Bah okay. Hey thanks Marty, I appreciate it.

ProPatriaMori

Note that the Cramster answer you link to does indeed show what Marty said--sigma k=11 to 40 is the sum of those equations from k=11 to 40.