# The CPU time requirement X

• Dec 14th 2009, 01:59 AM
zorro
The CPU time requirement X
Question : The CPU time requirement X of a typical job can be modelled by the following distribution

$P(X \le t)$ = $\alpha (1 - e_1^{\lambda_1 t})$ + $(1 - \alpha)(1 - e_2^{\lambda_2 t})$, where $\alpha = 0.6$, $\lambda_1 = 10$ and $\lambda_2 = 1.$

Compute
i) probability density function of X
ii) the mean service time
iii) Plot the distribution function and the density function of X.
• Dec 14th 2009, 02:53 AM
mr fantastic
Quote:

Originally Posted by zorro
Question : The CPU time requirement X of a typical job can be modelled by the following distribution

$P(X \le t)$ = $\alpha (1 - e_1^{\lambda_1 t})$ + $(1 - \alpha)(1 - e_2^{\lambda_2 t})$, where $\alpha = 0.6$, $\lambda_1 = 10$ and $\lambda_2 = 1.$

Compute
i) probability density function of X
ii) the mean service time
iii) Plot the distribution function and the density function of X.

Go back and revise your basic definitions.

You've been given the cdf: $F(t) = \Pr(X \leq t$.

i) By definition: pdf $= \frac{dF}{dt}$.

ii) By definition: mean $= \int_{0}^{+\infty} t f(t) \, dt = ....$

iii) Either use a graphics calculator or an on-line plotting program.
• Dec 17th 2009, 10:20 PM
zorro
Quote:

Originally Posted by mr fantastic
Go back and revise your basic definitions.

You've been given the cdf: $F(t) = \Pr(X \leq t$.

i) By definition: pdf $= \frac{dF}{dt}$.

ii) By definition: mean $= \int_{0}^{+\infty} t f(t) \, dt = ....$

iii) Either use a graphics calculator or an on-line plotting program.

Mr fantastic could u please provide me with some link where i could understand how to plot the density and distribution function on the graph....
• Dec 18th 2009, 01:54 AM
mr fantastic
Quote:

Originally Posted by zorro
Mr fantastic could u please provide me with some link where i could understand how to plot the density and distribution function on the graph....

Wolfram|Alpha
• Dec 18th 2009, 02:16 PM
zorro
Thank u Mr fantastic
Quote:

Originally Posted by mr fantastic

Thank u Mr fantastic and Merry Christmas(Toivo)(Music)
cheers mite (Beer)