4. Let the delay for a computer packets in the internet be modelled by T, which has the density (ct-0.5,0x}=1/2 c. Find the expected value of T, E[T] A4a Solve integral between 0 and 1 ct-0.5dt and find c=0.5 A4b= Solve integral between x and 1 0.5t-0.5dt and get t=1/4, A4c Integrate from 0 to 1 t times (0.5 t^-0.5) dx =1/3.

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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4.
Let the delay for a computer packets in the internet be modelled by T, which has the density
(ct-0.5,0<t≤1
function f(t) = 0, otherwize
a. Find the constant c, and sketch f(t) for 0 < t ≤ 2
b.
Find the median of T, which is the number x satisfying P{T>x}=1/2
c. Find the expected value of T, E[T]
A4a Solve integral between 0 and 1 ct-0.5dt and find c=0.5
A4b= Solve integral between x and 1 0.5t-0.5 dt and get t=1/4,
A4c Integrate from 0 to 1 t times (0.5 t^-0.5) dx =1/3.
Transcribed Image Text:4. Let the delay for a computer packets in the internet be modelled by T, which has the density (ct-0.5,0<t≤1 function f(t) = 0, otherwize a. Find the constant c, and sketch f(t) for 0 < t ≤ 2 b. Find the median of T, which is the number x satisfying P{T>x}=1/2 c. Find the expected value of T, E[T] A4a Solve integral between 0 and 1 ct-0.5dt and find c=0.5 A4b= Solve integral between x and 1 0.5t-0.5 dt and get t=1/4, A4c Integrate from 0 to 1 t times (0.5 t^-0.5) dx =1/3.
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