Math Help - CPU time requirement (probability)

1. CPU time requirement (probability)

The CPU time requirement X of a typical job can be modified by the following distribution

$P(X \le t) = \alpha (1-{e_1}^{-\lambda_1 t}) + (1-\alpha)(1-e^{-\lambda_2t})$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 density function of X.

2. Originally Posted by Stats
The CPU time requirement X of a typical job can be modified by the following distribution

$P(X \le t) = \alpha (1-{e_1}^{-\lambda_1 t}) + (1-\alpha)(1-e^{-\lambda_2t})$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 density function of X.
You have been given the cdf of X. Differentiate this with respect to t to get the pdf of X. Now answer the questions by using the usual definitions and formulas. It is assumed that you have the calculus background necesary to do the calculations.