# Thread: The CPU time requirement X

1. ## The CPU time requirement X

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

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

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

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

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

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: $\displaystyle F(t) = \Pr(X \leq t$.

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

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

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

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

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

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

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

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....

4. 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

5. ## Thank u Mr fantastic

Originally Posted by mr fantastic

Thank u Mr fantastic and Merry Christmas
cheers mite