The CPU time requirement X

**zorro** · December 14th 2009, 01:59 AM

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.

**mr fantastic** · December 14th 2009, 02:53 AM

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.

**zorro** · December 17th 2009, 10:20 PM

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....

**mr fantastic** · December 18th 2009, 01:54 AM

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

**zorro** · December 18th 2009, 02:16 PM

Originally Posted by mr fantastic

Wolfram|Alpha

Thank u Mr fantastic and Merry Christmas

cheers mite

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The CPU time requirement X

Some more info about plotting on the grap

Thank u Mr fantastic

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