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.