# [SOLVED] Probability/queue theory (a bit elementary)

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• May 5th 2010, 08:56 PM
bidii
[SOLVED] Probability/queue theory (a bit elementary)
Hey, I was wondering if this question looks right to you guys, because I cannot find a value for a other than 0 that will meet the requirements for a pdf. Please show me what I am overlooking. Thanks.

Measurements on a router indicate that the pdf of packet delay (in ms) is approxed by f(t)= $\displaystyle ae^{-a(t-2)}$, and the avg packet delay is 6ms.

So my qn is, do you guys see a valid value for a that can fulfil the requirements for the pdf? Thanks.
• May 5th 2010, 11:27 PM
CaptainBlack
Quote:

Originally Posted by bidii
Hey, I was wondering if this question looks right to you guys, because I cannot find a value for a other than 0 that will meet the requirements for a pdf. Please show me what I am overlooking. Thanks.

Measurements on a router indicate that the pdf of packet delay (in ms) is approxed by f(t)= $\displaystyle ae^{-a(t-2)}$, and the avg packet delay is 6ms.

So my qn is, do you guys see a valid value for a that can fulfil the requirements for the pdf? Thanks.

First you have not said that $\displaystyle t>2$ ms. Then any positive value of $\displaystyle a$ gives a pdf. So we have the mean is:

$\displaystyle \int_2^{\infty} t\ a\ e^{-a(t-2)}\; dt =2+\frac{1}{a}=6$

CB